


Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and realvalued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
Oscillations of First Order Linear Delay Difference Equations
Author(s):
G. E. Chatzarakis and I. P. Stavroulakis
Department of Mathematics, University of Ioannina,
451 10, Greece
ipstav@cc.uoi.gr
Abstract:
Consider the first order linear delay difference equation of the form _{} _{} where _{} is a sequence of nonnegative real numbers, k is a positive integer and _{} denotes the forward difference operator _{} New oscillation criteria are established when the wellknown oscillation conditions _{} and _{} are not satisfied. The results obtained essentially improve known results in the literature.
Paper's Title:
Integer Sums of Powers of Trigonometric Functions (MOD p), for prime p
Author(s):
G. J. Tee
Department of Mathematics, University of Auckland,
Auckland,
New Zealand
tee@math.auckland.ac.nz
Abstract:
Many multiparameter families of congruences (mod p) are found for integer sums of q^{th} powers of the trigonometric functions over various sets of equidistant arguments, where p is any prime factor of q. Those congruences provide sensitive tests for the accuracy of software for evaluating trigonometric functions to high precision.
Paper's Title:
A Low Order LeastSquares Nonconforming Finite Element Method for Steady Magnetohydrodynamic Equations
Author(s):
Z. Yu, D. Shi and H. Zhu
College of Science,
Zhongyuan
University of Technology,
Zhengzhou 450007,
China.
Email:
5772@zut.edu.cn
School of Mathematics and Statistics,
Zhengzhou University,
Zhengzhou 450001,
China.
Email:
shi_dy@126.com
Mathematics Department,
University of Southern Mississippi,
Hattiesburg MS, 39406,
U.S.A
Email:
huiqing.zhu@usm.edu
Abstract:
A low order leastsquares nonconforming finite element (NFE) method is proposed for magnetohydrodynamic equations with EQ_{1}^{rot} element and zeroorder RaviartThomas element. Based on the above element's typical interpolations properties, the existence and uniqueness of the approximate solutions are proved and the optimal order error estimates for the corresponding variables are derived.
Paper's Title:
Essential Random Fixed Point Set of Random Operators
Author(s):
Ismat Beg
Centre for Advanced Studies in Mathematics,
Lahore University of Management Sciences (LUMS),
54792Lahore, PAKISTAN.
ibeg@lums.edu.pk
URL: http://web.lums.edu.pk/~ibeg
Abstract:
We obtain necessary and sufficient conditions for the existence of essential random fixed point of a random operator defined on a compact metric space. The structure of the set of essential random fixed points is also studied.
Paper's Title:
On the Generalized Inverse _{ } over Integral Domains
Author(s):
Yaoming Yu and Guorong Wang
College of Education, Shanghai Normal University
Shanghai 200234
People's Republic of China.
yuyaoming@online.sh.cn
grwang@shnu.edu.cn
Abstract:
In this paper, we study further the generalized inverse _{ } of a matrix A over an integral domain. We give firstly some necessary and sufficient conditions for the existence of the generalized inverse _{ }, an explicit expression for the elements of the generalized inverse _{ } and an explicit expression for the generalized inverse _{ }, which reduces to the {1} inverse. Secondly, we verify that the group inverse, the Drazin inverse, the MoorePenrose inverse and the weighted MoorePenrose inverse are identical with the generalized inverse _{ } for an appropriate matrix G, respectively, and then we unify the conditions for the existence and the expression for the elements of the weighted MoorePenrose inverse, the MoorePenrose inverse, the Drazin inverse and the group inverse over an integral domain. Thirdly, as a simple application, we give the relation between some rank equation and the existence of the generalized inverse _{ }, and a method to compute the generalized inverse _{ }. Finally, we give an example of evaluating the elements of _{ } without calculating _{ }.
Paper's Title:
Isoperimetric Inequalities for Dual Harmonic Quermassintegrals
Author(s):
Yuan Jun, Zao Lingzhi and Duan Xibo
School of Mathematics and Computer Science,
Nanjing Normal University, Nanjing, 210097,
China.
yuanjun_math@126.com
Department of Mathematics, Nanjing Xiaozhuang University,
Nanjing, 211171,
China.
lzhzhao@163.com
Department of Mathematics, Shandong Water Polytechnic,
Shandong, 276826,
China
dxb1111@sohu.com
Abstract:
In this paper, some isoperimetric inequalities for the dual harmonic quermassintegrals are established.
Paper's Title:
A Geometric Generalization of BusemannPetty Problem
Author(s):
Liu Rong and Yuan Jun
Shanghai Zhangjiang Group Junior Middle School,
Huo Xiang Road, Shanghai, 201203,
China
Abstract:
The norm defined by Busemann's inequality establishes a class of star body  intersection body. This class of star body plays a key role in the solution of BusemannPetty problem. In 2003, Giannapoulos [1] defined a norm for a new class of halfsection. Based on this norm, we give a geometric generalization of BusemannPetty problem, and get its answer as a result
Paper's Title:
Viability
Theory And Differential Lanchester Type Models For Combat.
Differential Systems.
Author(s):
G. Isac and A. Gosselin
Department Of
Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston,
Ontario, Canada K7k 7b4
isacg@rmc.ca
gosselina@rmc.ca
URL:
http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL:
http://www.rmc.ca/academic/math_cs/gosselin/index_e.html
Abstract:
In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.
Paper's Title:
On the Optimal Buckling Loads of Clamped Columns
Author(s):
Samir Karaa
Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36, Alkhod 123
Muscat, Sultanate of Oman
skaraa@squ.edu.om
URL: http://ajmaa.org/EditorsU/SKaraa.php
Abstract:
We consider the problem of determining the optimal shape of a clamped column of given length and volume, without minimum cross section constraints. We prove that the necessary condition of optimality derived by Olhoff and Rasmussen is sufficient when 0<α<1. The number alpha appears in Equation 2.1. For the case α =1 it is shown that the value 48 is optimal. We also determine the exact values of the optimal shape at the extremities, and take advantage of a robust nonlinear ordinary differential equation solver COLSYS to compute the optimal buckling load with a high accuracy.
Paper's Title:
On Stan Ulam and his Mathematics
Author(s):
Krzysztof Ciesielski and Themistocles M. Rassias
Mathematics Institute, Jagiellonian University,
Łjasiewicza 6,
30348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou
Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr
Abstract:
In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.
Paper's Title:
Topological Aspects of Scalarization in Vector Optimization Problems.
Author(s):
Peter I. Kogut, Rosanna Manzo and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University, Naukova
STR.,
13,
49010 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Universitŕ di Salerno,
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata,
Via Ponte don Melillo, 84084 Fisciano (SA),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan
STR., 2,
49010 Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vectorvalued mappings with a weakened property of lower semicontinuity. We also prove the existence of the socalled generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.
Paper's Title:
On Some Relations Among the Solutions of the Linear Volterra Integral Equations
Author(s):
Ismet Ozdemir and Faruk Temizer
Inönü Üniversitesi Eğitim Fakültesi,
44280Malatya,
Turkey
Abstract:
The sufficient conditions for y_{1}(x)≤ y_{2}(x) were given in [1] such that y_{m}(x)=f_{m}(x)+∫_{a}^{x} K_{m}(x, t)y_{m}(t)dt,(m=1,2) and x∈ [a, b]. Some properties such as positivity, boundedness and monotonicity of the solution of the linear Volterra integral equation of the form f(t)=1∫_{0}^{t}K(tτ)f(τ)dτ=1K*f, (0≤ t<∞) were obtained, without solving this equation, in [3,4,5,6]. Also, the boundaries for functions f', f'',..., f^{(n)},(n ∈ N) defined on the infinite interval [0, ∞) were found in [7,8].
In this work, for the given equation f(t)=1K* f and n≥ 2, it is derived that there exist the functions L_{2}, L_{3},..., L_{n} which can be obtained by means of K and some inequalities among the functions f, h_{2}, h_{3},..., h_{i} for i=2, 3,...., n are satisfied on the infinite interval [0, ∞), where h_{i} is the solution of the equation h_{i}(t)=1L_{i}* h_{i} and n is a natural number.
Paper's Title:
On a Class of Meromorphic Functions of Janowski Type Related with a Convolution Operator
Author(s):
Abdul Rahman S. Juma, Husamaldin I. Dhayea
Department of
Mathematics,
Alanbar University, Ramadi,
Iraq.
Email: dr_juma@hotmail.com
Department of Mathematics,
Tikrit University, Tikrit,
Iraq.
URL: husamaddin@gmail.com
Abstract:
In this paper, we have introduced and studied new operator $Q^{k}_{λ,m,γ} by the Hadamard product (or convolution) of two linear operators D^{k}_{λ} and I_{m,γ}, then using this operator to study and investigate a new subclass of meromorphic functions of Janowski type, giving the coefficient bounds, a sufficient condition for a function to belong to the considered class and also a convolution property. The results presented provide generalizations of results given in earlier works.
Paper's Title:
The Dynamics of an Ebola Epidemic Model with Quarantine of Infectives
Author(s):
Eliab Horub Kweyunga
Department of Mathematics,
Kabale University,
P.O.Box 317, Kabale,
Uganda.
Email: hkweyunga@kab.ac.ug
Abstract:
The recurrent outbreaks of ebola in Africa present global health challenges. Ebola is a severe, very fatal disease with case fatality rates of up to 90%. In this paper, a theoretical deterministic model for ebola epidemic with quarantine of infectives is proposed and analyzed. The model exhibits two equilibria; the disease free and endemic equilibrium points. The basic reproduction number, R_{0}, which is the main threshold, is obtained and the stability of the equilibrium points established. Using parameter values drawn from the 2014 West Africa ebola outbreak, a numerical simulation of the model is carried out. It is found that the dynamics of the model are completely determined by R_{0} and that a quarantine success rate of at least 70% is sufficient to contain the disease outbreak.
Paper's Title:
The Concept of Convergence for 2Dimensional Subspaces Sequence in Normed Spaces
Author(s):
M. Manuharawati, D. N. Yunianti, M. Jakfar
Mathematics Department, Universitas
Negeri Surabaya,
Jalan Ketintang Gedung C8,
Surabaya 60321,
Indonesia.
Email: manuharawati@unesa.ac.id,
dwiyunianti@unesa.ac.id,
muhammadjakfar@unesa.ac.id
Abstract:
In this paper, we present a concept of convergence of sequence, especially, of 2dimensional subspaces of normed spaces. The properties of the concept are established. As consequences of our definition in an inner product space, we also obtain the continuity property of the angle between two 2dimensional subspaces of inner product spaces.
Paper's Title:
Analytical and Numerical Solutions of the Inhomogenous Wave Equation
Author(s):
T. Matsuura and S. Saitoh
Department of Mechanical Engineering, Faculty of Engineering,
Gunma University, Kiryu 3768515, Japan
matsuura@me.gunmau.ac.jp
Department of Mathematics, Faculty of Engineering,
Gunma University, Kiryu 3768515, Japan
ssaitoh@math.sci.gunmau.ac.jp
Abstract:
In this paper, by a new concept and method we give approximate solutions of the inhomogenous wave equation on multidimensional spaces. Numerical experiments are conducted as well.
Paper's Title:
Norm Estimates for the Difference between Bochner’s Integral and the Convex Combination of Function’s Values
Author(s):
P. Cerone, Y.J. Cho, S.S. Dragomir, J.K. Kim, and S.S. Kim
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
pietro.cerone@vu.edu.au
URL:
http://rgmia.vu.edu.au/cerone/index.html
Department of
Mathematics Education, College of Education,
Gyeongsang National University, Chinju 660701, Korea
yjcho@nongae.gsnu.ac.kr
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Department of
Mathematics, Kyungnam University,
Masan,, Kyungnam 631701, Korea
jongkyuk@kyungnam.ac.kr
Department of
Mathematics, Dongeui University,
Pusan 614714, Korea
sskim@dongeui.ac.kr
Abstract:
Norm estimates are developed between the Bochner integral of a vectorvalued function in Banach spaces having the RadonNikodym property and the convex combination of function values taken on a division of the interval [a, b].
Paper's Title:
On Pseudo Almost Periodic Solutions to Some Neutral FunctionalDifferential Equations
Author(s):
Toka Diagana and Eduardo Hernández
Department of Mathematics, Howard University
2441 6th Street NW,
Washington DC 20059,
USA.
tdiagana@howard.edu
Departamento de Matemática, I.C.M.C. Universidade de Săo Paulo,
Caixa Postal
668, 13560970, Săo Carlos SP,
Brazil.
lalohm@icmc.sc.usp.br
Abstract:
This paper discusses the existence and uniqueness of pseudo almost periodic solutions to a class of partial neutral functionaldifferential equations. Under some suitable assumptions, existence and uniqueness results are obtained. An example is given to illustrate abstract results.
Paper's Title:
Existence Results for Perturbed Fractional Differential Inclusions
Author(s):
Y.K. Chang
Department of Mathematics,
Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People's
Republic of China
lzchangyk@163.com
Abstract:
This paper is mainly concerned with the following fractional differential inclusions with boundary condition
A sufficient condition is established for the existence of solutions of the above problem by using a fixed point theorem for multivalued maps due to Dhage. Our result is proved under the mixed generalized Lipschitz and Carathéodory conditions.
Paper's Title:
A Short Proof of an Open Inequality with PowerExponential Functions
Author(s):
Mitsuhiro Miyagi and Yusuke Nishizawa
General Education, Ube National College of
Technology,
Tokiwadai 2141, Ube,
Yamaguchi 7558555,
Japan
Email:
miyagi@ubek.ac.jp
yusuke@ubek.ac.jp
Abstract:
V. Cîrtoaje conjectured that a^{3b} + b^{3a} + ( (a b)/2 )^{4} ≤ 2 holds for all nonnegative numbers a and b with a +b =2. In this short note, we give a proof of the Cîrtoaje's conjecture with powerexponential functions.
Paper's Title:
The Effect of Harvesting Activities on PreyPredator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem
Author(s):
Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari
Department of Mathematics, Faculty of
Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
Email: muh.nurulhuda@fmipa.unmul.ac.id
fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id
Abstract:
This paper discussed preypredator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.
Paper's Title:
RiemannStieltjes Integrals and Some Ostrowski Type Inequalities
Author(s):
W. G. Alshanti
Department of General Studies,
Jubail University College,
KSA.
Email: shantiw@ucj.edu.sa
Abstract:
In this article, we investigate new integral inequalities of Ostrowski's type of various functional aspects. For mapping's second derivative, we assume two cases, namely, L_{1} and L_{∞} spaces. Moreover, for first derivative, we investigate two different characteristics, namely, bounded variation and locally Lipchitz continuity. Applications to special means and composite quadrature rules are also carried out.
Paper's Title:
An Integration Technique for Evaluating Quadratic Harmonic Sums
Author(s):
J. M. Campbell and K.W. Chen
Department of Mathematics and Statistics,
York University, 4700 Keele St, Toronto,
ON M3J 1P3,
Canada.
Email: jmaxwellcampbell@gmail.com
Department of Mathematics, University of Taipei,
No. 1, AiGuo West Road,
Taipei 10048, Taiwan.
Email: kwchen@uTaipei.edu.tw
URL:
https://math.utaipei.edu.tw/p/412108222.php
Abstract:
The modified Abel lemma on summation by parts has been applied in many ways recently to determine closedform evaluations for infinite series involving generalized harmonic numbers with an upper parameter of two. We build upon such results using an integration technique that we apply to ``convert'' a given evaluation for such a series into an evaluation for a corresponding series involving squared harmonic numbers.
Paper's Title:
On Vector Variational Inequality Problem in Terms of Bifunctions
Author(s):
C. S. Lalitha and Monika Mehta
Department of Mathematics, Rajdhani College,
University of Delhi, Raja Garden,
Delhi 110015, India
cslalitha@rediffmail.com
Department of Mathematics, Satyawati College,
University Of Delhi, Ashok Vihar,
PhaseIII, Delhi 110052, India
mridul_in@yahoo.com
Abstract:
In this paper, we consider a generalized vector variational inequality problem expressed in terms of a bifunction and establish existence theorems for this problem by using the concepts of cone convexity and cone strong quasiconvexity and employing the celebrated Fan's Lemma. We also give two types of gap functions for this problem.
Paper's Title:
Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
Johnny Henderson and Abdelghani Ouahab
Department of Mathematics, Baylor University,
Waco, Texas 767987328
USA.
Johnny_Henderson@baylor.edu
Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univsba.dz
Abstract:
In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of LeraySchauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of LeraySchauder type in Fréchet spaces.
Paper's Title:
Existence of Solutions for Third Order Nonlinear Boundary Value Problems
Author(s):
Yue Hu and Zuodong Yang
School of Mathematics and Computer Science, Nanjing Normal University, Jiangsu Nanjing 210097,
China.
huu3y2@163.com
College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046,
China.
zdyang_jin@263.net
yangzuodong@njnu.edu.cn
Abstract:
In this paper, the existence of solution for a class of third order quasilinear ordinary differential equations with nonlinear boundary value problems
(Φ_{p}(u"))'=f(t,u,u',u"), u(0)=A, u'(0)=B, R(u'(1),u"(1))=0
is established. The results are obtained by using upper and lower solution methods.
Paper's Title:
The Convergence of Modified MannIshikawa Iterations when Applied to an Asymptotically Pseudocontractive Map
Author(s):
S. Soltuz
Departamento de Matematicas, Universidad de Los Andes, Carrera 1
No. 18A10, Bogota,
Colombia
and
``T. Popoviciu" Institute of Numerical Analysis
ClujNapoca,
Romania
smsoltuz@gmail.com
URL:http://www.uniandes.edu.co/
Abstract:
We prove that under minimal conditions the modified Mann and Ishikawa iterations converge when dealing with an asymptotically pseudocontractive map. We give an affirmative answer to the open question from C.E. Chidume and H. Zegeye, Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings, J. Math. Anal. Appl., 278 (2003), 354366.
Paper's Title:
On a Subclass of Uniformly Convex Functions Defined by the DziokSrivastava Operator
Author(s):
M. K. Aouf and G. Murugusundaramoorthy
Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com
School of Science and Humanities, VIT University
Vellore  632014,
India.
gmsmoorthy@yahoo.com
Abstract:
Making use of the DziokSrivastava operator, we define a new subclass T^{l}_{m}([α_{1}];α,β) of uniformly convex function with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of closetoconvexity, starlikeness and convexity for functions belonging to the class T^{l}_{m}([α_{1}];α,β) . We consider integral operators associated with functions belonging to the class H^{l}_{m}([α_{1}];α,β) defined via the DziokSrivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class T^{l}_{m}([α_{1}];α,β) and we obtain properties associated with generalized fractional calculus operators.
Paper's Title:
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
Ellipses of Minimal Area and of Minimal Eccentricity Circumscribed About a Convex Quadrilateral
Author(s):
Alan Horwitz
Penn State University,
25 Yearsley Mill Rd.,
Media, PA 19063,
U.S.A
alh4@psu.edu
Abstract:
First, we fill in key gaps in Steiner's nice characterization of the most nearly circular ellipse which passes through the vertices of a convex quadrilateral, . Steiner proved that there is only one pair of conjugate directions, M_{1} and M_{2}, that belong to all ellipses of circumscription. Then he proves that if there is an ellipse, E, whose equal conjugate diameters possess the directional constants M_{1} and M_{2}, then E must be an ellipse of circumscription which has minimal eccentricity. However, Steiner does not show the existence or uniqueness of such an ellipse. We prove that there is a unique ellipse of minimal eccentricity which passes through the vertices of . We also show that there exists an ellipse which passes through the vertices of and whose equal conjugate diameters possess the directional constants M_{1} and M_{2}. We also show that there exists a unique ellipse of minimal area which passes through the vertices of . Finally, we call a convex quadrilateral, , bielliptic if the unique inscribed and circumscribed ellipses of minimal eccentricity have the same eccentricity. This generalizes the notion of bicentric quadrilaterals. In particular, we show the existence of a bielliptic convex quadrilateral which is not bicentric.
Paper's Title:
Generalized Efficient Solutions to One Class of Vector Optimization Problems in Banach Space
Author(s):
Peter I. Kogut, Rosanna Manzo, and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University,
Naukova str., 13,
49050 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Dipartimento di Ingegneria
Dell’informazione e Matematica Applicata,
Universitŕ di Salerno,
Via
Ponte
Don Melillo,
84084 Fisciano
(Sa),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan str., 2,
49010
Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in Banach spaces for essentially nonlinear operator equations with additional control and state constraints. We assume that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. Using the penalization approach we derive both sufficient and necessary conditions for the existence of efficient solutions of the above problems. We also prove the existence of the socalled generalized efficient solutions via the scalarization of some penalized vector optimization problem.
Paper's Title:
Approximation of Common Fixed Points of a Finite Family of Asymptotically Demicontractive Mappings in Banach Spaces
Author(s):
Yuchao Tang,^{ }Yong Cai, Liqun Hu and Liwei Liu
Department of Mathematics, NanChang University,
Nanchang 330031, P.R. China
Department of Mathematics, Xi'an Jiaotong University,
Xi'an 710049, P.R.
China
Abstract:
By virtue of new analytic techniques, we analyze and
study
several strong convergence theorems for the approximation of
common fixed points of asymptotically demicontractive mappings
via the multistep iterative sequence with errors in Banach
spaces. Our results improve and extend the corresponding ones
announced by Osilike , Osilike and Aniagbosor, Igbokwe, Cho et
al., Moore and Nnoli, Hu and all the others.
Paper's Title:
Necessary and Sufficient Conditions for Cyclic Homogeneous Polynomial Inequalities of Degree Four in Real Variables
Author(s):
Vasile Cirtoaje and Yuanzhe Zhou
Department of Automatic Control and Computers
University of Ploiesti
Romania.
vcirtoaje@upgploiesti.ro.
High School Affiliated to Wuhan University, China
Abstract:
In this paper, we give two sets of necessary and sufficient conditions that the inequality f_{4}(x,y,z) ≥ 0 holds for any real numbers x,y,z, where f_{4}(x,y,z) is a cyclic homogeneous polynomial of degree four. In addition, all equality cases of this inequality are analysed. For the particular case in which f_{4}(1,1,1)=0, we get the main result in [3]. Several applications are given to show the effectiveness of the proposed methods.
Paper's Title:
Asymptotic Analysis of Positive Decreasing Solutions of a Class of Systems of Second Order Nonlinear Differential Equations in the Framework of Regular Variation
Author(s):
Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa
Department of Mathematical Analysis and
Numerical Mathematics,
Faculty of Mathematics, Physics and Informatics,
Comenius Universiy, 842 48 Bratislava,
Slovakia.
Email: ksntksjm4@gmail.com
Professor Emeritus at: Hiroshima
University,
Department of Mathematics, Faculty of Science,
HigashiHiroshima 7398526,
Japan.
Email: jaros@fmph.uniba.sk
Department of Mathematics, Faculty of
Education,
Kumamoto University, Kumamoto 8608555,
Japan.
Email:
tanigawa@educ.kumamotou.ac.jp
Abstract:
The system of nonlinear differential equations
is under consideration, where α_{i}
and β_{i} are positive constants and
p_{i}(t) and q_{i}(t) are continuous regularly varying functions
on [a,∞). Two kinds of criteria are established for
the existence of strongly decreasing regularly varying solutions with negative
indices of (A) with precise asymptotic behavior at infinity. Fixed point
techniques and basic theory of regular variation are utilized for this purpose.
Paper's Title:
Inequalities for Discrete FDivergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated fdivergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of KullbackLeibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the fdivergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
Integrating Factors and First Integrals of a Class of Third Order Differential Equations
Author(s):
Mohammadkheer AlJararha
Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: mohammad.ja@yu.edu.jo
Abstract:
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor exists which transforms it to an exact one. Hence, it can be reduced into a second order differential equation. In this paper, we give explicit forms for certain integrating factors of a class of the third order differential equations.
Paper's Title:
A Method of the Study of the Cauchy Problem for~a~Singularly Perturbed Linear Inhomogeneous Differential Equation
Author(s):
E. E. Bukzhalev and A. V. Ovchinnikov
Faculty of Physics,
Moscow State University,
1 Leninskie Gory,
Moscow, 119991,
Russia
Email: bukzhalev@mail.ru
Russian Institute for Scientific and
Technical Information of the Russian Academy of Sciences,
20 Usievicha St., Moscow, 125190,
Russia
Email: ovchinnikov@viniti.ru
Abstract:
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the deviation (in the norm of the space of continuous functions) of its nth element from the solution of the problem is proportional to the (n+1)th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.
Paper's Title:
On Finding Integrating Factors and First Integrals for a Class of Higher Order Differential Equations
Author(s):
Mohammadkheer M. AlJararha
Department of Mathematics,
Yarmouk University,
Irbid, 21163,
Jordan.
Email: mohammad.ja@yu.edu.jo
Abstract:
If the $nth$ order differential equation is not exact, under certain
conditions, an integrating factor exists which transforms the differential
equation into an exact one. Thus, the order of differential equation can be
reduced to the lower order. In this paper, we present a technique for finding
integrating factors of the following class of differential equations:
Here, the functions F_{0},F_{1},F_{2},
…,F_{n} are assumed to be continuous
functions with their first partial derivatives on some simply connected domain
Ω ⊂ R^{n+1}.
We also presented some demonstrative examples
Paper's Title:
On a New Class of Eulerian's Type Integrals Involving Generalized Hypergeometric Functions
Author(s):
Sungtae Jun, Insuk Kim and Arjun K. Rathie
General Education Institute,
Konkuk University, Chungju 380701,
Republic of Korea.
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com
Abstract:
Very recently MasjedJamei and Koepf established interesting and useful generalizations of various classical summation theorems for the _{2}F_{1}, _{3}F_{2}, _{4}F_{3}, _{5}F_{4} and _{6}F_{5} generalized hypergeometric series. The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases have also been given.
Paper's Title:
On an extension of Edwards's double integral with applications
Author(s):
I. Kim, S. Jun, Y. Vyas and A. K. Rathie
Department of Mathematics Education,
Wonkwang University,
Iksan, 570749,
Republic of Korea.
General Education Institute,
Konkuk University,
Chungju 380701,
Republic of Korea.
Department of Mathematics, School of
Engineering,
Sir Padampat Singhania University,
Bhatewar, Udaipur, 313601, Rajasthan State,
India.
Department of Mathematics,
Vedant College of Engineering and Technology,
(Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: iki@wku.ac.kr
sjun@kku.ac.kr
yashoverdhan.vyas@spsu.ac.in
arjunkumarrathie@gmail.com
Abstract:
The aim of this note is to provide an extension of the well known and useful Edwards's double integral. As an application, new class of twelve double integrals involving hypergeometric function have been evaluated in terms of gamma function. The results are established with the help of classical summation theorems for the series _{3}F_{2} due to Watson, Dixon and Whipple. Several new and interesting integrals have also been obtained from our main findings.
Paper's Title:
On the Polyconvolution of Hartley Integral Transforms H_{1}, H_{2}, H_{1} and Integral Equations
Author(s):
Nguyen Minh Khoa and Dau Xuan Luong
Department of Mathematics,
Electric Power University,
Ha Noi, and Faculty of Fundamental Science,
Ha Long University, Quang Ninh,
Viet Nam.
Email: khoanm@epu.edu.vn,
dauxuanluong@gmail.com
Abstract:
In this paper, we construct and study a new polyconvolution * (f,g,h)(x) of functions f, g, h. We will show that the polyconvolution satisfy the following factorization equality
H_{1}[*(f,g,h)](y)=(H_{2}f)(y)(H_{1}g)(y)(H_{1}h)(y), ∀y∈ R.
We prove the existence of this polyconvolution in the space L(R). As examples, applications to solve an integral equation of polyconvolution type and two systems of integral equations of polyconvolution type are presented.
Paper's Title:
Bounds on the Jensen Gap, and Implications for MeanConcentrated Distributions
Author(s):
Xiang Gao, Meera Sitharam, Adrian E. Roitberg
Department of Chemistry, and Department
of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
Email: qasdfgtyuiop@gmail.com
URL:
https://scholar.google.com/citations?user=t2nOdxQAAAAJ
Abstract:
This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.
Paper's Title:
Some fixed point results in partial Smetric spaces
Author(s):
M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: Rezaee.mohammad.m@gmail.com
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: sedghi.gh@qaemiau.ac.ir
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: mukheimer@psu.edu.sa
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: kamal@psu.edu.sa
Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
Email: zoran.mitrovic@tdtu.edu.vn
Abstract:
We introduce in this article a new class of generalized metric spaces, called partial Smetric spaces. In addition, we also give some interesting results on fixed points in the partial Smetric spaces and some applications.
Paper's Title:
Numerical Approximation by the Method of Lines with Finitevolume Approach of a Solute Transport Equation in Periodic Heterogeneous Porous Medium
Author(s):
D. J. Bambi Pemba and B. Ondami
Université Marien Ngouabi,
Factuté des Sciences et Techniques,
BP 69, Brazzaville,
Congo.
Email: bondami@gmail.com
Abstract:
In this paper we are interested in the numerical approximation of a twodimensional solute transport equation in heterogeneous porous media having periodic structures. It is a class of problems which has been the subject of various works in the literature, where different methods are proposed for the determination of the socalled homogenized problem. We are interested in this paper, in the direct resolution of the problem, and we use the method of lines with a finite volume approach to discretize this equation. This discretization leads to an ordinary differential equation (ODE) that we discretize by the Euler implicit scheme. Numerical experiments comparing the obtained solution and the homogenized problem solution are presented. They show that the precision and robustness of this method depend on the ratio between, the mesh size and the parameter involved in the periodic homogenization.
Paper's Title:
Solving NonAutonomous Nonlinear Systems of Ordinary Differential Equations Using MultiStage Differential Transform Method
Author(s):
K. A. Ahmad, Z. Zainuddin, F. A. Abdullah
School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia.
Email: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my
Abstract:
Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multistage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and RungeKutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the RungeKutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations
Paper's Title:
Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design
Author(s):
Mohammadkheer M. AlJararha And Jehad M. AlJararha
Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: mohammad.ja@yu.edu.jo
Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: jehad@yu.edu.jo
Abstract:
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities can be used to generalize different probability distribution functions. Also, they can be used to generalize some statistical designs, e.g., the probability proportional to the size without replacement design.
Paper's Title:
Rational Expressions of Arithmetic and Geometric Means for the Sequence n^{p}_{n ∈ N} and the Geometric Progression
Author(s):
M. Kinegawa, S. Miyamoto and Y. Nishizawa
Faculty of Education, Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email: m.kinegawa.645@ms.saitamau.ac.jp
Faculty of Education, Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email: s.miyamoto.245@ms.saitamau.ac.jp
Faculty of Education, Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email:
ynishizawa@mail.saitamau.ac.jp
Abstract:
In this paper, we consider the arithmetic and geometric means for the sequence n^{p}_{n ∈ N} and the geometric progression. We obtain the results associated with the rational expressions of the means.
Paper's Title:
Evaluation of a New Class of Double Integrals Involving Generalized Hypergeometric Function _{4}F_{3}
Author(s):
Joohyung Kim, Insuk Kim and Harsh V. Harsh
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: joohyung@wku.ac.kr
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: iki@wku.ac.kr
Department of Mathematics, Amity School
of Eng. and Tech.,
Amity University Rajasthan
NH11C, Jaipur303002, Rajasthan,
India.
Email: harshvardhanharsh@gmail.com
Abstract:
Very recently, Kim evaluated some double integrals involving a generalized hypergeometric function _{3}F_{2} with the help of generalization of Edwards's wellknown double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. In this research paper we evaluate one hundred double integrals involving generalized hypergeometric function _{4}F_{3} in the form of four master formulas (25 each) viz. in the most general form for any integer. Some interesting results have also be obtained as special cases of our main findings.
Paper's Title:
Oscillatory Behavior of SecondOrder NonCanonical Retarded Difference Equations
Author(s):
G.E. Chatzarakis^{1}, N. Indrajith^{2}, E. Thandapani^{3} and K.S. Vidhyaa^{4}
^{1}Department
of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
Email: gea.xatz@aspete.gr,
geaxatz@otenet.gr
^{2}Department
of Mathematics,
Presidency College, Chennai  600 005,
India.
Email: indrajithna@gmail.com
^{3}Ramanujan
Institute for Advanced Study in Mathematics,
University of Madras,
Chennai  600 005,
India.
Email: ethandapani@yahoo.co.in
^{4}Department of
Mathematics,
SRM Easwari Engineering College,
Chennai600089,
India.
Email: vidyacertain@gmail.com
Abstract:
Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the secondorder noncanonical difference equation with retarded argument
Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.
Paper's Title:
New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
Author(s):
S. S. Dragomir
School of Computer Science and Mathematics, Victoria
University of Technology, PO BOX
14428, MCMC 8001, VICTORIA, AUSTRALIA.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Abstract:
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.
Paper's Title:
On an Extension of Hilbert’s Integral Inequality with Some Parameters
Author(s):
Bicheng Yang
Department of
Mathematics, Guangdong Education College, Guangzhou, Guangdong 510303, People’s
Republic of China.
bcyang@pub.guangzhou.gd.cn
URL:
http://www1.gdei.edu.cn/yangbicheng/index.html
Abstract:
In this paper, by introducing some parameters and estimating the weight function, we give an extension of Hilbert’s integral inequality with a best constant factor. As applications, we consider the equivalent form and some particular results.
Paper's Title:
FeketeSzegö Inequality for Certain Class of Analytic Functions
Author(s):
V. Ravichandran, Maslina Darus, M. Hussain Khan, and K. G. Subramanian
School of
Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm, Penang, Malaysia
vravi@cs.usm.my
School of
Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Banki 43600, Malaysia
maslina@pkrisc.cc.ukm.my
Department of
Mathematics, Islamiah College,
Vaniambadi 635 751, India
Department of
Mathematics, Madras Christian College, Tambaram,
Chennai 600 059, India
kgsmani@vsnl.net
Abstract:
In this present investigation, the authors obtain FeketeSzegö inequality for a certain class of analytic functions f(z) for which lies in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain application of our main result for a class of functions defined by Hadamard product (convolution) is given. As a special case of our result we obtain FeketeSzegö inequality for a class of functions defined through fractional derivatives. Also we obtain FeketeSzegö inequality for the inverse functions.
Paper's Title:
Reverses of the Triangle Inequality in Inner Product Spaces
Author(s):
Sever S. Dragomir
School of Computer Science and Mathematics,
Victoria University Of Technology,
PO Box 14428, Mcmc 8001,
Victoria, Australia.
sever@csm.vu.edu.au
Url:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Abstract:
Some new reverses for the generalised triangle inequality in inner product spaces are given. Applications in connection to the Schwarz inequality and for vectorvalued integrals are provided as well.
Paper's Title:
Positive Solution For Discrete ThreePoint Boundary Value Problems
Author(s):
WingSum Cheung And Jingli Ren
Department of Mathematics,
The University of Hong Kong,
Pokfulam, Hong Kong
wscheung@hku.hk
Institute of Systems Science,
Chinese Academy of Sciences,
Beijing 100080, P.R. China
renjl@mx.amss.ac.cn
Abstract:
This paper is concerned with the existence of positive solution to the discrete threepoint boundary value problem
_{
},
_{
}
where _{ }, and f is allowed to change sign. By constructing available operators, we shall apply the method of lower solution and the method of topology degree to obtain positive solution of the above problem for _{ } on a suitable interval. The associated Green’s function is first given.
Paper's Title:
A Simple New Proof of FanTausskyTodd Inequalities
Author(s):
ZhiHua Zhang and ZhenGang Xiao
Zixing Educational Research Section,
Chenzhou City, Hunan 423400, P. R. China.
Zhihua Zhang
Url: http://www.hnzxslzx.com/zzhweb/
Department Of Mathematics, Hunan Institute Of Science And Technology,
Yueyang City, Hunan 423400, P. R. China.
Zhengang Xiao
Abstract:
In this paper we present simple new proofs of the inequalities:
_{ }
which holds for all real numbers a_{0} = 0, a_{1}, · · · , a_{n}, a_{n+1} = 0 and the coefficients 2(1  cos(π/(n + 1))) and 2(1 + cos(π/(n + 1))) are the best possible; and
_{ }
which holds for all real numbers a_{0} = 0, a_{1}, · · · , a_{n} and the coefficients 2(1cos(π/(2n + 1))) and 2(1 + cos(π/(2n + 1))) are the best possible.
Paper's Title:
Weak Solution for Hyperbolic Equations with a NonLocal Condition
Author(s):
Lazhar Bougoffa
King Khalid
University, Faculty of Science, Department of Mathematics,
P.O.Box 9004, Abha, Saudi Arabia
abogafah@kku.edu.sa
Abstract:
In this paper, we study hyperbolic equations with a nonlocal condition. We prove the existence and uniqueness of weak solutions, using energy inequality and the density of the range of the operator generated by the problem.
Paper's Title:
Meromorphic PValent Functions With Positive And Fixed Second Coefficients
Author(s):
B.A. Frasin and G. Murugusundaramoorthy
Department of Mathematics,
Al AlBayt University,
P.O. Box: 130095,
Mafraq, Jordan.
bafrasin@yahoo.com
URL: http://www.geocities.com/bafrasin/techie.html
Department of Mathematics,
Vellore Institute of Technology,
Deemed University,
Vellore  632014,
India.
gmsmoorthy@yahoo.com
Abstract:
We introduce the classes _{} and _{ }of meromorphic univalent functions ith positive and fixed second coefficients. The aim of the present paper is to obtain coefficient inequalities and closure theorems for these classes. Furthermore, the radii of convexity and starlikeness for functions the classes _{} and _{} are determined.
Paper's Title:
The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations
Author(s):
Alexandru Mihai Bica
Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro
Abstract:
We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.
Paper's Title:
On Zeros of Diagonally Quasiconvex Multifunctions
Author(s):
Zoran D. Mitrović
Faculty of Electrical Engineering,
University of Banja Luka,
78000 Banja Luka, Patre 5
Bosnia and Herzegovina
zmitrovic@etfbl.net
Abstract:
In this paper, we extended the notion of diagonally quasiconvexity for multifunctions and established several existence results for zeros of diagonally quasiconvex multifunctions. As applications we obtain the results of fixed points, coincidence points and best approximations for multifunctions. Using our result we also prove the existence of solutions to the variationallike inequality problem and generalized vector equilibrium problem. The results of this paper generalize some known results in the literature.
Paper's Title:
Positive Periodic TimeScale Solutions for Functional Dynamic Equations
Author(s):
Douglas R. Anderson and Joan Hoffacker
Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
andersod@cord.edu
URL: http://www.cord.edu/faculty/andersod/
Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
johoff@clemson.edu
URL: http://www.math.clemson.edu/facstaff/johoff.htm
Abstract:
Using Krasnoselskii's fixed point theorem, we establish the existence of positive periodic solutions to two pairs of related nonautonomous functional delta dynamic equations on periodic time scales, and then extend the discussion to higherdimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.
Paper's Title:
Notes on Sakaguchi Functions
Author(s):
Shigeyoshi Owa, Tadayuki Sekine and Rikuo Yamakawa
Department of Mathematics, Kinki University,
HigashiOsaka, Osaka 5778502,
Japan.
owa@math.kindai.ac.jp
Office of Mathematics, College of Pharmacy, Nihon University,
71 Narashinodai, Funabashicity,
Chiba, 2748555, Japan.
tsekine@pha.nihonu.ac.jp
Department of Mathematics, Shibaura Institute of Technology,
Minuma, Saitamacity,
Saitama 3378570, Japan.
yamakawa@sic.shibaurait.ac.jp
Abstract:
By using the definition for certain univalent functions f(z) in the open unit disk U given by K. Sakaguchi [2], two classes S(α) and T(α) of analytic functions in U are introduced. The object of the present paper is to discuss some properties of functions f(z) belonging to the classes S(α) and T(α).
Paper's Title:
Boundary Value Problems for Fractional DiffusionWave equation
Author(s):
Varsha DaftardarGejji and Hossein Jafari
Department of Mathematics, University of Pune,
Ganeshkhind, Pune  411007,
INDIA.
vsgejji@math.unipune.ernet.in
jafari_h@math.com
Abstract:
Non homogeneous fractional diffusionwave equation has been solved under linear/nonlinear boundary conditions. As the order of time derivative changes from
0 to 2, the process changes from slow diffusion to classical diffusion to mixed diffusionwave behaviour.
Numerical examples presented here confirm this inference. Orthogonality of eigenfunctions in case of fractional StürmLiouville problem has been established
Paper's Title:
Uniqueness of Meromorphic Functions that Share Three Values
Author(s):
Abhijit Banerjee
Department of Mathematics
Kalyani Government Engineering College
West Bengal 741235
India.
abanerjee_kal@yahoo.co.in
abanerjee@mail15.com
abanerjee_kal@rediffmail.com
Abstract:
In the paper dealing with the uniqueness problem of meromorphic functions we prove five theorems one of which will improve a result given by Lahiri \cite{5} and the remaining will supplement some previous results.
Paper's Title:
A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials
Author(s):
I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić
Department of Applied Mathematics, Faculty of Electrical
Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr
School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir
Faculty of Applied Technical Sciences, University of Prishtina,
Mother
Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000
Zagreb,
Croatia
pecaric@hazu.hr
Abstract:
A reverse of the triangle inequality in inner product spaces related to the celebrated DiazMetcalf inequality with applications for complex polynomials is given.
Paper's Title:
On the FeketeSzegő Inequality for Some Subclasses of Analytic Functions
Author(s):
T.N. Shanmugam and A. Singaravelu
Department of Mathematics,
College of Engineering,
Anna University, Chennai600 025,
Tamilnadu, India
shan@annauniv.edu
Department of Mathematics,
Valliammai Engineering College,
Chennai603 203,
Tamilnadu, India
sivasaisastha@rediffmail.com
Abstract:
In this present investigation, the authors obtainFeketeSzegő's inequality for certain normalized analytic functions _{} defined on the open unit disk for which _{} lie in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, FeketeSzegő's inequality for a class of functions defined through fractional derivatives is also obtained.
Paper's Title:
Komatu Integral Transforms of Analytic Functions Subordinate to Convex Functions
Author(s):
T. N. Shanmugam and C. Ramachandran
Department of Mathematics, College of Engineering,
Anna University, Chennai600 025, Tamilnadu,
India
shan@annauniv.edu
Department of Mathematics, College of Engineering,
Anna University, Chennai600 025, Tamilnadu,
India
crjsp2004@yahoo.com
Abstract:
In this paper, we consider the class A of the functions f(z) of the form
which are analytic in an open disk
and study certain subclass of the class A, for which
has some property. Certain inclusion and the closure properties like convolution with convex univalent function etc. are studied.
Paper's Title:
A Coefficient Inequality For Certain Subclasses of Analytic Functions Related to Complex Order
Author(s):
B. Srutha Keerthi, B. Adolf Stephen and S. Sivasubramanian
Department Of Applied Mathematics, Sri Venkateswara College Of Engineering, Anna University,
Sriperumbudur, Chennai  602 105,
India.
laya@svce.ac.in
Department of Mathematics, Madras Christian College,
Chennai  600059,
India
adolfmcc2003@yahoo.co.in
Department of Mathematics, College of Engineering, Anna University,
Tamilnadu, Chennai  600 025,
India.
sivasaisastha@rediffmail.com
Abstract:
In this present investigation, the authors obtain coefficient inequality for certain normalized analytic functions of complex order f(z) defined on the open unit disk for which _{ } (_{ } and _{} be a complex number) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions of complex order defined by convolution are given. As a special case of this result, coefficient inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the coefficient inequalities of the subclasses of starlike and convex functions of complex order.
Paper's Title:
Construction of Lyapunov Functionals In Functional Differential Equations With Applications To Exponential Stability In Volterra Integrodifferential Equations
Author(s):
Youssef N. Raffoul
Department of Mathematics, University of Dayton,
Dayton OH 454692316,
USA
youssef.raffoul@notes.udayton.edu
URL:http://academic.udayton.edu/YoussefRaffoul
Abstract:
Nonnegative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee the exponential asymptotic stability and uniform exponential asymptotic stability of the zero solution of nonlinear functional differential systems. The theory is applied to Volterra integrodifferential equations in the form of proposition examples.
Paper's Title:
On Oscillation of SecondOrder Delay Dynamic Equations on Time Scales
Author(s):
S. H. Saker
Department of Mathematics, Faculty of Science,
Mansoura University, Mansoura, 35516,
Egypt.
shsaker@mans.edu.eg
Abstract:
Some new oscillation criteria for secondorder linear delay dynamic equation on a time scale T are established. Our results improve the recent results for delay dynamic equations and in the special case when T=R, the results include the oscillation results established by Hille [1948, Trans. Amer. Math. Soc. 64 (1948), 234252] and Erbe [Canad. Math. Bull. 16 (1973), 4956.] for differential equations. When T=Z the results include and improve some oscillation criteria for difference equations. When T=hZ, h>0, T=q^{N} and T=N^{2}, i.e., for generalized second order delay difference equations our results are essentially new and can be applied on different types of time scales. An example is considered to illustrate the main results.
Paper's Title:
Some Inequalities for a Certain Class of Multivalent Functions Using Multiplier Transformation
Author(s):
K. Suchithra, B. Adolf Stephen, A. Gangadharan and S. Sivasubramanian
Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai  602105,
India.
suchithravenkat@yahoo.co.in
Department Of Mathematics,
Madras Christian College
Chennai  600059,
India.
adolfmcc2003@yahoo.co.in
Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai  602105,
India.
ganga@svce.ac.in
Department Of Mathematics,
Easwari Engineering College
Ramapuram, Chennai  600089,
India.
ganga@svce.ac.in
Abstract:
The object of the present paper is to derive several inequalities associated with differential subordinations between analytic functions and a linear operator defined for a certain family of pvalent functions, which is introduced here by means of a family of extended multiplier transformations. Some special cases and consequences of the main results are also considered.
Paper's Title:
Multivalent Harmonic Mappings Convoluted With a Multivalent Analytic Function
Author(s):
Om P. Ahuja and Özlem Güney
Kent State University, Department of Mathematical Sciences,
14111, ClaridonTroy Road, Burton, Ohio 44021,
U.S.A.
oahuja@kent.edu
University of Dicle, Department of Mathematics,
Faculty of Science and Art, 21280 Diyarbakir,
Turkey
ozlemg@dicle.edu.tr
Abstract:
The object of this paper is to study certain geometric properties of a family of multivalent harmonic mappings in the plane convoluted with a multivalent analytic function in the open unit disc.
Paper's Title:
A Subclass of Meromorphically Multivalent Functions with Applications to Generalized Hypergeometric Functions
Author(s):
M. K. Aouf
Mathematics Department,
Faculty of Science,
Mansoura University 35516,
Egypt
mkaouf127@yahoo.com
Abstract:
In this paper a new subclass of meromorphically multivalent functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically pvalent functions. The main object of the present paper is to investigate the various important properties and characteristics of this subclass of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to this subclass. Also we consider several applications of our main results to generalized hypergeomtric functions.
Paper's Title:
Ulam Stability of Functional Equations
Author(s):
Stefan Czerwik and Krzysztof Król
Institute of Mathematics
Silesian University of Technology
Kaszubska 23,
44100 Gliwice,
Poland
Stefan.Czerwik@polsl.pl
Krzysztof.Krol@polsl.pl
Abstract:
In this survey paper we present some of the main results on UlamHyersRassias stability for important functional equations.
Paper's Title:
On the product of Mmeasures in lgroups
Author(s):
A. Boccuto, B. Riěcan, and A. R. Sambucini
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I06123 Perugia,
Italy.
boccuto@dipmat.unipg.it
URL:
http://www.dipmat.unipg.it/~boccuto
Katedra Matematiky, Fakulta Prírodných Vied,
Univerzita Mateja Bela,
Tajovského, 40, Sk97401 Banská Bystrica,
Slovakia.
riecan@fpv.umb.sk
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I06123 Perugia,
Italy.
matears1@unipg.it
URL:
http://www.unipg.it/~matears1
Abstract:
Some extensiontype theorems and compactness
properties for the
product of lgroupvalued Mmeasures are proved.
Paper's Title:
Asymptotic Distribution of Products of Weighted Sums of Dependent Random Variables
Author(s):
Y. Miao and J. F. Li
College
of Mathematics
and Information
Science,
Henan Normal
University
Henan,
China
yumiao728@yahoo.com.cn
College
of Mathematics
and Information
Science,
Henan Normal
University, 453007
Henan,
China.
junfen_li@yahoo.com.cn
Abstract:
In this paper we establish the asymptotic distribution of products of weighted sums of dependent positive random variable, which extends the results of Rempała and Wesołowski (2002).
Paper's Title:
Fractional Integral Operators and Olsen Inequalities on NonHomogeneous Spaces
Author(s):
Idha Sihwaningrum, Herry P. Suryawan, Hendra Gunawan
Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia
hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Abstract:
We prove the boundedness of the fractional integral operator I_{α} on generalized Morrey spaces of nonhomogeneous type. In addition, we also present Olsentype inequalities for a multiplication operator involving I_{α}. Our proof uses a result of GarcíaCuerva and Martell [3].
Paper's Title:
Real Interpolation Methods and Quasilogarithmic Operators
Author(s):
Ming Fan
School of Industrial Technology and Management,
Dalarna University, 781 88 Borlänge, Sweden
fmi@du.se
URL: http://users.du.se/~fmi
Abstract:
The purpose of this paper is to deal with nonlinear quasilogarithmic operators, which possesses the uniformly bounded commutator property on various interpolation spaces in the sense of BrudnyiKrugljak associated with the quasipower parameter spaces. The duality, and the domain and range spaces of these operators are under consideration. Some known inequalities for the Lebesgue integration spaces and the trace classes are carried over to the noncommutative symmetric spaces of measurable operators affiliated with a semifinite von Neumann algebra.
Paper's Title:
Hardy Type Inequalities via Convexity  The Journey so Far
Author(s):
James A.
Oguntuase and LarsErik Persson
Department of Mathematics,
University of Agriculture,
P. M. B. 2240, Abeokuta, Nigeria.
Department of
Mathematics, Luleĺ University of Technology,
SE971 87, Luleĺ , Sweden.
oguntuase@yahoo.com,
larserik@sm.luth.se .
Abstract:
It is nowadays wellknown that Hardy's inequality (like many other inequalities) follows directly from Jensen's inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.
Paper's Title:
On an Elliptic OverDetermined Problem in Dimension Two
Author(s):
Lakhdar Ragoub
Department of Mathematics and Information of Tiyadhechnology
AL Yamamah University
P.O. Box 45 180, Riyadh 11 512
Saudi Arabia.
Abstract:
We extend the method of Weinberger for a
nonlinear overdetermined elliptic problem
in R^{2}.
We prove that the domain in consideration is a ball. The
tool of this investigation are maximum principles and Pfunctions.
Paper's Title:
On Opial's Inequality for Functions of nIndependent Variables
Author(s):
S. A. A. ElMarouf and S. A. ALOufi
Department of Mathematics,
Faculty of Science,
Minoufiya University,
Shebin ElKoom,
Egypt
Department of Mathematics,
Faculty of Science, Taibah University,
Madenahmonwarah,
Kingdom of Saudia Arabia
Abstract:
In this paper, we introduce Opial inequalities for functions of nindependent variables. Also, we discuss some different forms of Opial inequality containing functions of n independent variables and their partial derivatives with respect to independent variables.
Paper's Title:
Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
M. Lakrib, A. Oumansour and K. Yadi
Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbčs 22000, Algérie
mlakrib@univsba.dz
oumansour@univsba.dz
Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univtlemcen.dz
Abstract:
In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.
Paper's Title:
Stability Problems for Generalized Additive Mappings and EulerLagrange Type Mappings
Author(s):
M. Todoroki, K. Kumahara, T. Miura and S.E. Takahasi
The Open University of Japan,
Chiba, 2618586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp
Yamagata University,
Yonezawa 9928510,
Japan
miura@yz.yamagatau.ac.jp
Toho University, Yamagata University,
Chiba, 2730866,
Japan
sin_ei1@yahoo.co.jp
Abstract:
We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of EulerLagrange type mappings obtained by H. M. Kim, K. W. Jun and J. M. Rassias.
Paper's Title:
Szegö Limits and Haar Wavelet Basis
Author(s):
M. N. N. Namboodiri and S. Remadevi
Dept. of Mathematics, Cochin University
of Science and Technology,
Cochin21, Kerala,
India.
Dept. of Mathematics, College of
Engineering,
Cherthala, Kerala,
India.
Abstract:
This paper deals with Szegö type limits for multiplication operators on L^{2} (R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators T_{f} using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class of multiplication operators T_{f} , f∈ L^{∞} (R) with respect to Haar (wavelet) system with appropriate ordering. More general classes of orderings of Haar system are identified for which the Szegö type limit exist for certain classes of multiplication operators. Some illustrative examples are also provided.
Paper's Title:
Some Identities for Ramanujan  Göllnitz  Gordon Continued fraction
Author(s):
M. S. Mahadeva Naika, B. N. Dharmendra and S. Chandan Kumar
Department of Mathematics,
Bangalore University,
Central College Campus,
Bangalore560 001,
INDIA
Department of Mathematics,
Maharani's Science College for Women,
J. L. B. Road, Mysore570 001,
INDIA
Abstract:
In this paper, we obtain certain PQ etafunction identities, using which we establish identities providing modular relations between RamanujanGöllnitzGordon continued fraction H(q) and H(q^n) for n= 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 19, 23, 25, 29 and 55.
Paper's Title:
To a Banach *algebra in a Semipartial Dynamical System
Author(s):
Bahman Tabatabaie Shourijeh and Seyed Mostafa Zebarjad
Department of Mathematics,
College of Sciences,
Shiraz University, Shiraz 71454,
Iran.
Email:
tabataba@math.susc.ac.ir
zebarjad@mail.yu.ac.ir
URL:
http://research.shirazu.ac.ir/faculty/More.asp?ID=207
Abstract:
By a partial dynamical system, we mean a triple containing a C*algebra A, a discrete group G and a partial action of G on A. There are two C*algebras associated to a given partial dynamical system. These are nothing but the certain C*completions of a Banach *algebra. In constructing such a Banach *algebra, usually, a tedious limit process is used to apply. In this paper, we prove some theorems in this context without any limit process.
Paper's Title:
On Eigenvalues and Boundary Curvature of the C*algebra Numerical Rang
Author(s):
M. T. Heydari
Department of Mathematics,
College of Sciences,
Yasouj University,
Yasouj, 7591474831,
Iran.
Email: heydari@yu.ac.ir
Abstract:
Let A be a C*algebra with unit 1 and a∈A be a nilpotent. By Donoghue's Theorem, all corner points of its numerical range V(a) belong to the spectrum σ(a). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂ V(a) of V(a) to σ(a) should be in some sense bounded by the radius of curvature of ∂ V(a) at p.
Paper's Title:
The boundedness of BesselRiesz operators on generalized Morrey spaces
Author(s):
Mochammad Idris, Hendra Gunawan and Eridani
Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
Email:
mochidris@students.itb.ac.id
Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
Email: hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Department of Mathematics,
Airlangga University,
Surabaya 60115,
Indonesia.
Email: eridani.dinadewi@gmail.com
Abstract:
In this paper, we prove the boundedness of BesselRiesz operators on generalized Morrey spaces. The proof uses the usual dyadic decomposition, a Hedbergtype inequality for the operators, and the boundedness of HardyLittlewood maximal operator. Our results reveal that the norm of the operators is dominated by the norm of the kernels.
Paper's Title:
Stability of the DBar Reconstruction Method for Complex Conductivities
Author(s):
^{1}S. El Kontar, ^{1}T. El Arwadi, ^{1}H. Chrayteh, ^{2}J.M. SacÉpée
^{1}Department of Mathematics and
Computer Science,
Faculty of Science, Beirut Arab University,
P.O. Box: 115020, Beirut,
Lebanon.
Email: srs915@student.bau.edu.lb
^{2}Institut Élie Cartan de
Lorraine,
Université de Lorraine  Metz,
France.
Abstract:
In 2000, Francini solved the inverse conductivity problem for twicedifferentiable conductivities and permittivities. This solution was considered to be the first approach using Dbar methods with complex conductivities. In 2012, based on Francini's work, Hamilton introduced a reconstruction method of the conductivity distribution with complex values. The method consists of six steps. A voltage potential is applied on the boundary. Solving a DBar equation gives the complex conductivity. In this paper, the stability of the DBar equation is studied via two approximations, t^{exp} and t^{B}, for the scattering transform. The study is based on rewriting the reconstruction method in terms of continuous operators. The conductivity is considered to be non smooth.
Paper's Title:
A Note on Divergent Fourier Series and λPermutations
Author(s):
A. Castillo, J. Chavez and H. Kim
Tufts University,
Department of Mathematics,
Medford, MA 02155,
USA
Email: angel.castillo@tufts.edu
Texas Tech University,
Department of Mathematics and Statistics,
Lubbock, TX 79409,
USA
Email: josechavez5@my.unt.edu
University of MichiganDearborn,
Department of Mathematics and Statistics,
Dearborn, MI 48128,
USA.
Email: khyejin@umich.edu
Abstract:
We present a continuous function on [π,π] whose Fourier series diverges and it cannot be rearranged to converge by a λpermutation.
Paper's Title:
Existence of Positive Solutions for Nonlinear Fractional Differential Equations with Multipoint Boundary Conditions
Author(s):
N. Adjeroud
Khenchela University, Department of
Mathematics,
Khenchela, 40000,
Algeria.
Email: adjnac@gmail.com
Abstract:
This paper is devoted to the existence results of positive solutions for a nonlinear fractional differential equations with multipoint boundary conditions. By means of the Schauder fixed point theorem, some results on the existence are obtained.
Paper's Title:
Polyanalytic Functions on Subsets of Z[i]
Author(s):
Abtin Daghighi
Linköping University,
SE581 83,
Sweden.
Email: abtindaghighi@gmail.com
Abstract:
For positive integers q we consider the kernel of the powers L^{q} where L is one of three kinds of discrete analogues of the CauchyRiemann operator. The first two kinds are wellstudied, but the third kind less so. We give motivations for further study of the third kind especially since its symmetry makes it more appealing for the cases q≥ 2.
From an algebraic perspective it makes sense that the chosen multiplication on the kernels is compatible with the choice of pseudopowers. We propose such multiplications together with associated pseudopowers. We develop a prooftool in terms of certain sets of uniqueness.
Paper's Title:
Fractional class of analytic functions Defined Using qDifferential Operator
Author(s):
K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan
Department of Mathematics and
Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
Email: kr_karthikeyan1979@yahoo.com
College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
Email: musthafa.ibrahim@gmail.com
Department of Mathematics, Presidency
College (Autonomous),
Chennai600005, Tamilnadu,
India.
Abstract:
We define a qdifferential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving qdifferential fractional operator. We also determine the necessary and sufficient conditions for functions to be in the class. Further, we obtain the coefficient estimates, extreme points, growth and distortion bounds.
Paper's Title:
On Commutator of Aluthge Transforms and FugledePutnam Property
Author(s):
(Manzar Maleki, Ali Reza Janfada and Seyed Mohammad Sadegh Nabavi Sales
International Campus, Faculty of
Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad,
Iran.
Email: manzar.maleki@gmail.com
Faculty of Mathematics and Statistics,
Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,
Iran.
Email: ajanfada@birjand.ac.ir
Department of Pure Mathematics, Hakim
Sabzevari University,
P.O. Box 397, Sabzevar,
Iran.
Email: sadegh.nabavi@hsu.ac.ir
Abstract:
We deal with the wellknown FugledePutnam theorem and related FPproperty. We show that if (A,B) has the FPproperty, then so has where 0≤ t_{1},t_{2}≤1 are arbitrary. We first prove that if and only if AX=XB for all X, whenever (A,B) has the FPproperty. We prove some similar results for instead of $ as well. Also we introduce the sequence of generalized iterations of Aluthge transform of operators and express some results for this notion associated to the FPproperty.
Paper's Title:
An Analytical Solution of Perturbed Fisher's Equation Using Homotopy Perturbation Method (HPM), Regular Perturbation Method (RPM) and Adomian Decomposition Method (ADM)
Author(s):
Moussa Bagayogo, Youssouf Minoungou, Youssouf Pare
Departement de Mathematique,
Universite Ouaga I Pr Joseph KiZerbo,
Burkina Faso.
Email:
moussabagayogo94@gmail.com,
m.youl@yahoo.fr,
pareyoussouf@yahoo.fr.
Abstract:
In this paper, Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian decomposition Method (ADM) are applied to Fisher equation. Then, the solution yielding the given initial conditions is gained. Finally, the solutions obtained by each method are compared
Paper's Title:
Dynamical Analysis of HIV/AIDS Epidemic Model with Two Latent Stages, Vertical Transmission and Treatment
Author(s):
Nur Shofianah, Isnani Darti, Syaiful Anam
Mathematics Department,Faculty of
Mathematics and Natural Sciences.
University of Brawijaya,
Jl. Veteran, Malang 65145,
Indonesia.
Email:
nur_shofianah@ub.ac.id,
isnanidarti@ub.ac.id,
syaiful@ub.ac.id
Abstract:
We discuss about dynamical analysis of HIV/AIDS epidemic model with two latent stages, vertical transmission and treatment. In this model, the spreading of HIV occurs through both horizontal and vertical transmission. There is also treatment for individual who has been HIV infected. The latent stage is divided into slow and fast latent stage based on the immune condition which varies for each individual. Dynamical analysis result shows that the model has two equilibrium points: the diseasefree equilibrium point and the endemic equilibrium point. The existence and global stability of equilibrium points depend on the basic reproduction number R_{0}. When R_{0} <1, only the diseasefree equilibrium point exists. If R_{0} >1, there are two equilibrium points, which are the diseasefree equilibrium point and the endemic equilibrium point. Based on the result of stability analysis, the diseasefree equilibrium point is globally asymptotically stable if R_{0} <1, while if R_{0} > 1 and p=q, the endemic equilibrium point will be globally asymptotically stable. In the end, we show some numerical simulations to support the analytical result.
Paper's Title:
An Existence of the Solution to Neutral Stochastic Functional Differential Equations Under the Holder Condition
Author(s):
YoungHo Kim
Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnamdo 51140,
Korea.
Email: iyhkim@changwon.ac.kr
Abstract:
In this paper, we show the existence and uniqueness of solution of the neutral stochastic functional differential equations under weakened H\"{o}lder condition, a weakened linear growth condition, and a contractive condition. Furthermore, in order to obtain the existence of a solution to the equation we used the Picard sequence.
Paper's Title:
Weyl's theorem for class Q and k  quasi class Q Operators
Author(s):
S. Parvatham and D. Senthilkumar
Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore10, Tamilnadu,
India.
Email: parvathasathish@gmail.com
Post Graduate and Research Department of
Mathematics,
Govt. Arts College, Coimbatore641018, Tamilnadu,
India.
Email: senthilsenkumhari@gmail.com
Abstract:
In this paper, we give some properties of class Q operators. It is proved that every class Q operators satisfies Weyl's theorem under the condition that T^{2} is isometry. Also we proved that every k quasi class Q operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every k quasi class Q operators.
Paper's Title:
On Ruled Surfaces According to QuasiFrame in Euclidean 3Space
Author(s):
M. Khalifa Saad and R. A. AbdelBaky
Department of Mathematics, Faculty of
Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email:
mohamed_khalifa77@science.sohag.edu.eg,
mohammed.khalifa@iu.edu.sa
Department of Mathematics, Faculty of
Science,
Assiut University, Assiut,
EGYPT.
Email: rbaky@live.com
Abstract:
This paper aims to study the skew ruled surfaces by using the quasiframe of Smarandache curves in the Euclidean 3space. Also, we reveal the relationship between SerretFrenet and quasiframes and give a parametric representation of a directional ruled surface using the quasiframe. Besides, some comparative examples are given and plotted which support our method and main results.
Paper's Title:
Antiderivatives and Integrals Involving Incomplete Beta Functions with Applications
Author(s):
R. AlAhmad^{1,2} and H. Almefleh^{1}
Mathematics Department,
Yarmouk University,
Irbid 21163,
Jordan.
Email: rami_thenat@yu.edu.jo
Faculty of Engineering,
Higher Colleges of Technology,
Ras Alkhaimah,
UAE.
Abstract:
In this paper, we prove that incomplete beta functions are antiderivatives of several products and powers of trigonometric functions, we give formulas for antiderivatives for products and powers of trigonometric functions in term of incomplete beta functions, and we evaluate integrals involving trigonometric functions using incomplete beta functions. Also, we extend some properties of the beta functions to the incomplete beta functions. As an application for the above results, we find the moments for certain probability distributions.
Paper's Title:
Reduced Generalized Combination Synchronization Between Two nDimensional IntegerOrder Hyperchaotic Systems and One mDimensional FractionalOrder Chaotic System
Author(s):
Smail Kaouache, Mohammed Salah Abdelouahab and Rabah Bououden
Laboratory of Mathematics and their
interactions,
Abdelhafid Boussouf University Center, Mila.
Algeria
Email: smailkaouache@gmail.com,
medsalah3@yahoo.fr,
rabouden@yahoo.fr
Abstract:
This paper is devoted to investigate the problem of reduced generalized combination synchronization (RGCS) between two ndimensional integerorder hyperchaotic drive systems and one mdimensional fractionalorder chaotic response system. According to the stability theorem of fractionalorder linear system, an active mode controller is proposed to accomplish this end. Moreover, the proposed synchronization scheme is applied to synchronize three different chaotic systems, which are the Danca hyperchaotic system, the modified hyperchaotic Rossler system, and the fractionalorder RabinovichFabrikant chaotic system. Finally, numerical results are presented to fit our theoretical analysis.
Paper's Title:
Existence and Approximation of Traveling Wavefronts for the Diffusive MackeyGlass Equation
Author(s):
C. RamirezCarrasco and J. MolinaGaray
Facultad de Ciencias Basicas,
Universidad Catolica del Maule, Talca,
Chile
Email: carloshrc1989@gmail.com
molina@imca.edu.pe
Abstract:
In this paper, we consider the diffusive MackeyGlass model with discrete delay. This equation describes the dynamics of the blood cell production. We investigate the existence of traveling wavefronts solutions connecting the two steady states of the model. We develop an alternative proof of the existence of such solutions and we also demonstrate the existence of traveling wavefronts moving at minimum speed. The proposed approach is based on the use technique of upperlower solutions. Finally, through an iterative procedure, we show numerical simulations that approximate the traveling wavefronts, thus confirming our theoretical results.
Paper's Title:
Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators
Author(s):
B. Deruni^{1}, A. S. Hacinliyan^{1,2}, E. Kandiran^{3}, A. C. Keles^{2}, S. Kaouache^{4}, M.S. Abdelouahab^{4}, N.E. Hamri^{4}
^{1}Department
of Physics,
University of Yeditepe,
Turkey.
^{2}Department
of Information Systems and Technologies,
University of Yeditepe,
Turkey
^{3}Department
of Software Development,
University of Yeditepe,
Turkey.
^{4}Laboratory
of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.
Email:
berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centrunivmila.dz
medsalah3@yahoo.fr
n.hamri@centreunivmila.dz
Abstract:
In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.
Paper's Title:
Pointwise Convergence of Fouriertype Series with Exponential Weights
Author(s):
Hee Sun Jung and Ryozi Sakai
Department of Mathematics Education,
Sungkyunkwan University,
Seoul 110745,
Republic of Korea.
Email: hsun90@skku.edu
Department of Mathematics,
Meijo University, Nagoya 4688502,
Japan.
Email: ryozi@hm.aitai.ne.jp
Abstract:
Let R = (  ∞,∞), and let Q∈C^{1}(R):R→[0,∞) be an even function. We consider the exponential weights w(x)=e^{Q(x)}, x∈R. In this paper we obtain a pointwise convergence theorem for the Fouriertype series with respect to the orthonormal polynomials {p_{n}(w^{2};x)}.
Paper's Title:
On Euler's First Transformation Formula for khypergeometric Function
Author(s):
Sungtae Jun and Insuk Kim
General Education Institute,
Konkuk University, Chungju 380701,
Republic of Korea.
Email: sjun@kku.ac.kr
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Email: iki@wku.ac.kr
Abstract:
Mubeen et al. obtained Kummer's first transformation for the khypergeometric function. The aim of this note is to provide the Eulertype first transformation for the khypergeometric function. As a limiting case, we recover the results of Mubeen et al. In addition to this, an alternate and easy derivation of Kummer's first transformation for the khypergeometric function is also given.
Paper's Title:
Hankel Functional Connected to Lemniscate of Bernoulli
Author(s):
K. Ramanuja Rao, Rajnesh Lal and Kaushal Singh
Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
Email: ramanuja.kotti@fnu.ac.fj
rajnesh.lal@fnu.ac.fj
kaushal.singh@fnu.ac.fj
Abstract:
The aim of present paper is to derive a higher bound (HB) of 3^{rd} order Hankel determinant for a collection of holomorphic mappings connected with exactly to the right side of the lemniscate of Bernoulli, whose polar coordinates form is r^{2} = 2cos^{2}(2θ). The method carried in this paper is more refined than the method adopted by the authors (see [1]), who worked on this problem earlier.
Paper's Title:
Locally Bicomplex Convex Module and Their Applications
Author(s):
Stanzin Kunga and Aditi Sharma
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
Email: stanzinkunga19@gmail.com
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
Email: aditi.sharmaro@gmail.com
Abstract:
Let X be a locally BC convex module and L(X) be the family of all continuous bicomplex linear operators on X. In this paper, we study some concepts of Dvalued seminorms on locally BC convex module. Further, we study the bicomplex version of C_{o} and (C_{o},1) semigroup. The work of this paper is inspired by the work in [2] and [6].
Paper's Title:
Algorithms for Nonlinear Problems Involving Strictly Pseudocontractive Mappings
Author(s):
Mathew Olajiire Aibinu^{1}, Surendra Colin Thakur^{2}, Sibusiso Moyo^{3}
^{1}Institute for Systems Science
& KZN ESkill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
^{1}DSINRF
Centre of Excellence in Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: moaibinu@yahoo.com
mathewa@dut.ac.za
^{2} KZN ESkill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
Email: thakur@dut.ac.za
^{3}Institute for Systems Science & Office of the DVC Research,
Innovation & Engagement Milena Court,
Durban University of Technology,
Durban 4000,
South Africa.
Email: dvcrie@dut.ac.za
Abstract:
The puzzles in approximating a fixed point of nonlinear problems involving the class of strictly pseudocontractive mappings are conquered in this paper through viscosity implicit rules. Using generalized contraction mappings, a new viscosity iterative algorithm which is implicit in nature is proposed and analysed in Banach spaces for the class of strictly pseudocontractive mappings. The computations and analysis which are used in the proposed scheme are easy to follow and this gives rooms for a broad application of the scheme. It is obtained that the proposed iterative algorithm converges strongly to a fixed point of a μstrictly pseudocontractive mapping which also solves a variational inequality problem. The result is also shown to hold for finite family of strictly pseudocontractive mappings. A numerical example is given to show the skillfulness of the proposed scheme and its implementation.
Paper's Title:
A Review on Minimally Supported Frequency Wavelets
Author(s):
K Pallavi^{1}, M C Lineesh^{1}, A Noufal^{2}
^{1}Department of
Mathematics,
National Institute of Technology Calicut,
Kerala 673601,
India.
Email:
pavikrishnakumar@gmail.com
lineesh@nitc.ac.in
^{2}Department of Mathematics,
Cochin University of Science and Technology,
Kerala 682022,
India.
Email: noufal@cusat.ac.in
Abstract:
This paper provides a review on Minimally Supported Frequency (MSF) wavelets that includes the construction and characterization of MSF wavelets. The characterization of MSF wavelets induced from an MRA is discussed and the nature of the lowpass filter associated with it is explained. The concept of wavelet set and dimension function is introduced to study this class of wavelets. Along with MSF wavelets, selementary wavelets and unimodular wavelets are also considered due to the similarity in definitions. Examples and illustrations are provided for more clarity.
Paper's Title:
On General Class of Nonlinear Contractive Maps and their Performance Estimates
Author(s):
Olalekan Taofeek Wahab and Salaudeen Alaro Musa
Department of Mathematics and
Statistics
Kwara State University, Malete
P. M. B. 1530 Ilorin,
Nigeria.
Email: taofeek.wahab@kwasu.edu.ng
Abstract:
This paper considers two independent general class of nonlinear contractive maps to study the existence properties of nonlinear operators with prior degenerate. The existence properties are proved in the framework of approximate fixed points with the imposition of the general class of contractive conditions in metrical convex spaces without emphasis on completeness or compactness. For computational purposes, the performance estimates and the sensitivity dependence of these conditions are obtained for the Picard operator. Practical examples are also considered to justify the validity of the conditions. The results ensure no term is lost in the operators with prior degenerate and the conditions are strictly larger class when compare with others in the literature.
Paper's Title:
On Trigonometric Approximation of Continuous Functions by Deferred Matrix Means
Author(s):
Xhevat Zahir Krasniqi
Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë
10000,
Republic of Kosovo.
Email: xhevat.krasniqi@unipr.edu
URL:
https://staff.unipr.edu/profile/xhevatkrasniqi
Abstract:
In this paper, for the first time, we introduce the deferred matrix means which contain the wellknown generalized deferred Nörlund, deferred Nörlund, deferred Riesz, deferred Cesŕro means introduced earlier by others, and a new class of sequences (predominantly a wider class than the class of Head Bounded Variation Sequences). In addition, using the deferred matrix means of Fourier series of a continuous function, we determine the degree of approximation of such function via its modulus of continuity and a positive mediate function.
Paper's Title:
Three Inequalities Associated with Rado Inequality
Author(s):
Rin Miyao, Yusuke Nishizawa, Keigo Takamura
Faculty of Education,
Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email: r.miyao.242@ms.saitamau.ac.jp
Faculty of Education,
Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email:
ynishizawa@mail.saitamau.ac.jp
Faculty of Education,
Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email: k.takamura.442@ms.saitamau.ac.jp
Abstract:
In this short note we estimate three inequalities associated with Rado inequality and show the refinement and reverse of Arithmetic mean Geometric mean inequality.
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