


Paper's Title:
Comparison Results for Solutions of Time Scale Matrix Riccati Equations and Inequalities
Author(s):
R. Hilscher
Department of Mathematical Analysis, Faculty of Science,
Masaryk University, Janáčkovo nám. 2a,
CZ60200, Brno, Czech Republic.
hilscher@math.muni.cz
URL: http://www.math.muni.cz/~hilscher/
Abstract:
In this paper we derive comparison results for Hermitian solutions of time scale matrix Riccati equations and Riccati inequalities. Such solutions arise from special conjoined bases (X,U) of the corresponding time scale symplectic system via the Riccati quotient _{}. We also discuss properties of a unitary matrix solution _{} of a certain associated Riccati equation.
Paper's Title:
Shape Diagrams for 2D Compact Sets  Part I: Analytic Convex Sets.
Author(s):
S. Rivollier, J. Debayle and J.C. Pinoli
Ecole Nationale Supérieure des Mines de SaintEtienne,
CIS  LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional compact convex sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow thirtyone shape diagrams to be built. Most of these shape diagrams can also been applied to more general compact sets than compact convex sets. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these thirtyone shape diagrams. The purpose of this paper is to present the first part of this study, by focusing on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The second and third part of the comparative study are published in two following papers [19.20]. They are focused on analytic simply connected sets and convexity discrimination for analytic and discretized simply connected sets, respectively.
Paper's Title:
Iterative Approximation of Common Fixed Points of a Finite Family of Asymptotically Hemicontractive Type Mappings
Author(s):
JuiChi Huang
Center for General Education,
Northern Taiwan Institute of Science and Technology,
Peito, Taipei,
Taiwan, 11202, R.O.C.
juichi@ntist.edu.tw
Abstract:
In this paper, we prove that the sequence of
the modified IshikawaXu,
IshikawaLiu, MannXu and MannLiu iterative types of a finite family of
asymptotically hemicontractive type mappings converges strongly to a common
fixed point of the family in a real puniformly convex Banach space with
p>1. Our results improve and extend some recent results.
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:
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:
C*valued metric projection and MoorePenrose inverse on Hilbert C*modules
Author(s):
M. Eshaghi Gordji, H. Fathi and S.A.R. Hosseinioun
Department of Mathematics,
Semnan University, P.O. Box 35195363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
Email: Madjid.Eshaghi@gmail.com
Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
Email: Hedayat.fathi@yahoo.com
Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
Email: shossein@uark.net
Abstract:
Let t be a regular operator between Hilbert C^{*}modules and t^{†} be its MoorePenrose inverse. We give some characterizations for t^{†} based on C^{*}valued metric projection. MoorePenrose inverse of bounded operators and elements of a C^{*}algebra is studied as a special case.
Paper's Title:
MSplit Equality for Monotone Inclusion Problem and Fixed Point Problem in Real Banach Spaces
Author(s):
^{1,2}Christian Chibueze Okeke, ^{3}Abdumalik Usman Bello, ^{1}Chinedu Izuchukwu, and ^{1}Oluwatosin Temitope Mewomo
^{1}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: okekec@ukzn.ac.za
Email: izuchukwuc@ukzn.ac.za
Email: mewomoo@ukzn.ac.za
^{2}DSTNRF
Center of Excellence in Mathematical and Statistical Sciences (CoEMass)
Johannesburg,
South Africa.
^{3}Federal
University,
DutsinMa, Katsina State,
Nigeria.
Email:
uabdulmalik@fudutsinma.edu.ng
Abstract:
In this paper a new iterative algorithm for approximating a common solution of split equality monotone inclusion problem and split equality fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality monotone inclusion problem and the set of solutions of a split equality fixed point problem for right Bregman strongly nonexpansive mappings in the setting of puniformly convex Banach spaces which are also uniformly smooth. We also give some applications.
Paper's Title:
An Algorithm to Compute GaussianType Quadrature Formulae
that Integrate Polynomials and Some Spline Functions Exactly
Author(s):
Allal Guessab
Laboratoire de Mathématiques Appliquées,
Université de Pau, 64000, Pau,
France.
allal.guessab@univpau.fr
URL: http://www.univpau.fr/~aguessab/
Abstract:
It is wellknown that for sufficiently smooth integrands on an interval, numerical integration can be performed stably and efficiently via the classical (polynomial) Gauss quadrature formulae. However, for many other sets of integrands these quadrature formulae do not perform well. A very natural way of avoiding this problem is to include a wide class among arbitrary functions (not necessary polynomials) to be integrated exactly. The spline functions are natural candidates for such problems. In this paper, after studying Gaussian type quadrature formulae which are exact for spline functions and which contain boundary terms involving derivatives at both end points, we present a fast algorithm for computing their nodes and weights. It is also shown, taking advantage of the close connection with ordinary Gauss quadrature formula, that the latter are computed, via eigenvalues and eigenvectors of real symmetric tridiagonal matrices. Hence a new class of quadrature formulae can then be computed directly by standard software for ordinary Gauss quadrature formula. Comparative results with classical Gauss quadrature formulae are given to illustrate the numerical performance of the approach.
Paper's Title:
On Convergence Theorems of an Implicit Iterative Process with Errors for a Finite Family of Asymptotically quasi Inonexpansive Mappings
Author(s):
Farrukh Mukhamedov and Mansoor Saburov
Department of Computational & Theoretical
Sciences,
Faculty of Sciences, International Islamic University Malaysia,
P.O. Box, 141, 25710, Kuantan,
Malaysia
Abstract:
In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {T_{j}}^{N}_{i=1} of asymptotically quasi I_{j}nonexpansive mappings as well as a family of {Ij}^{N}_{j=1} of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existing literature.
Paper's Title:
Cubic Alternating Harmonic Number Sums
Author(s):
Anthony Sofo
Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
Email:
Anthony.Sofo@vu.edu.au
Abstract:
We develop new closed form representations of sums of cubic alternating harmonic numbers and reciprocal binomial coefficients. We also identify a new integral representation for the ζ (4) constant.
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:
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:
Iterative Approximation of Zeros of Accretive Type Maps, with Applications
Author(s):
Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo
African University of Science and
Technology, Abuja,
Nigeria.
Email: cchidume@aust.edu.ng
Email: chinedu.ezea@gmail.com
Email: mrzzaka@yahoo.com
Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
Email: chinedu.ezea@gmail.com
Ebonyi State University,
Abakaliki,
Nigeria
Email: mrzzaka@yahoo.com
Abstract:
Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E→ E^{*} be the normalized duality map on E and let A:E^{*}→ E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)^{1}(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u^{*} in (AJ)^{1}(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, nontrivial examples of maps A for which AJ is accretive are presented..
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:
An Approximation of Jordan Decomposable Functions for a Lipschitz Function
Author(s):
Ibraheem Alolyan
Mathematics Department,
College of Science, King Saud University
P.O.Box: 2455, Riyadh 11451,
Saudi Arabia
ialolyan05@yahoo.com
Abstract:
The well known Jordan decomposition theorem gives the useful characterization that any function of bounded variation can be written as the difference of two increasing functions. Functions which can be expressed in this way can be used to formulate an exclusion test for the recent Cellular Exclusion Algorithms for numerically computing all zero points or the global minima of functions in a given cellular domain [2,8,9]. In this paper we give an algorithm to approximate such increasing functions when only the values of the function of bounded variation can be computed. For this purpose, we are led to introduce the idea of εincreasing functions. It is shown that for any Lipschitz continuous function, we can find two εincreasing functions such that the Lipschitz function can be written as the difference of these functions.
Paper's Title:
Properties of Certain Multivalent Functions Involving Ruscheweyh Derivatives
Author(s):
NEng Xu and DingGong Yang
Department of Mathematics,
Changshu Institute of Technology,
Changshu, Jiangsu 215500,
China
Abstract:
Let A_{p}(p∈ N) be the class of functions which are analytic in the unit disk. By virtue of the Ruscheweyh derivatives we introduce the new subclasses C_{p}(n,α,β,λ,μ) of A_{p}. Subordination relations, inclusion relations, convolution properties and a sharp coefficient estimate are obtained. We also give a sufficient condition for a function to be in C_{p}(n,α,β,λ,μ)
Paper's Title:
Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of Jnonexpansive Maps with Applications
Author(s):
Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea
African University of Science and
Technology,
Abuja,
Nigeria.
Email:
cchidume@aust.edu.ng
Ebonyi State University,
Abakaliki,
Nigeria.
Email: mrzzaka@yahoo.com
Nnamdi Azikiwe University,
Awka,
Nigeria.
Email: chinedu.ezea@gmail.com
Abstract:
Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^{*}. Let {T_{i}}^{∞}_{i=1} be a family of Jnonexpansive maps, where, for each i,~T_{i} maps E to 2^{E*}. A new class of maps, Jnonexpansive maps from E to E^{*}, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common Jfixed points of {T_{i}}^{∞}_{i=1} is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x^{*} in ∩^{∞}_{n=1}F_{J}T_{i}. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.
Paper's Title:
A New Method with Regularization for Solving Split Variational Inequality Problems in Real Hilbert Spaces
Author(s):
Francis Akutsah^{1} and Ojen Kumar Narain^{2}
^{1}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
^{2}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
Abstract:
In this paper, we introduce a new inertial extrapolation method with regularization for approximating solutions of split variational inequality problems in the frame work of real Hilbert spaces. We prove that the proposed method converges strongly to a minimumnorm solution of the problem without using the conventional two cases approach. In addition, we present some numerical experiments to show the efficiency and applicability of the proposed method. The results obtained in this paper extend, generalize and improve several results in this direction.
Paper's Title:
Inequalities Relating to the Gamma Function
Author(s):
ChaoPing Chen and Feng Qi
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
chenchaoping@hpu.edu.cn
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
qifeng@hpu.edu.cn,
fengqi618@member.ams.org
Url:
http://rgmia.vu.edu.au/qi.html,
http://dami.hpu.edu.cn/qifeng.html
Abstract:
For _{}, we have
_{ }.
For_{},
_{ },
And equality occurs for x=1.
Paper's Title:
Fixed Point Theorems for a Finite Family of Asymptotically Nonexpansive Mappings
Author(s):
E. Prempeh
Department of Mathematics,
Kwame Nkrumah University of Science and Technology,
Kumasi, Ghana
edward_prempeh2000@yahoo.com
Abstract:
Let _{} be a real reflexive Banach space with a uniformly Gâteaux differentiable norm, _{} be a nonempty bounded closed convex subset of _{} i=1,2,...,r be a finite family of asymptotically nonexpansive mappings such that for each _{} Let _{ } be a nonempty set of common fixed points of _{} and define
_{} . Let _{} be fixed and let _{} be such that _{} as _{} . We can prove that the sequence _{} satisfying the relation_{} associated with _{} , converges strongly to a fixed point of _{} provided _{} possesses uniform normal structure. Furthermore we prove that the iterative process: _{} _{}
_{} , converges strongly to a fixed point of _{}
Paper's Title:
Positive Solutions for Systems of Threepoint Nonlinear Boundary Value Problems
Author(s):
J. Henderson and S. K. Ntouyas
Department of Mathematics, Baylor University
Waco, Texas
767987328 USA.
Johnny_Henderson@baylor.edu
URL: http://www3.baylor.edu/~Johnny_Henderson
Department of Mathematics, University of Ioannina
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas
Abstract:
Values of λ are determined for which there exist positive solutions of the system of threepoint boundary value problems, u''(t)+ λa(t)f(v(t))=0, v''(t)+λb(t)g(u(t))=0, for 0 < t <1, and satisfying, u(0) = 0, u(1)=α u(η), v(0) = 0, v(1)=α v(η). A GuoKrasnosel'skii fixed point theorem is applied.
Paper's Title:
On a Method of Proving the HyersUlam Stability of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchorąźych 2,
30084 Kraków,
Poland
jbrzdek@ap.krakow.pl
Abstract:
We show that generalizations of some (classical) results on the HyersUlam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable
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:
New Implicit KirkType Schemes for General Class of QuasiContractive Operators in Generalized Convex Metric Spaces
Author(s):
K. Rauf, O. T. Wahab and A. Ali
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
Email: krauf@unilorin.edu.ng
Department of Statistics and Mathematical
Sciences,
Kwara State University, Malete,
Nigeria.
Department of Mathematics,
Mirpur University of Science and Technology, Mirpur,
Pakistan.
Abstract:
In this paper, we introduce some new implicit Kirktype iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasicontractive type operators. The strong convergence, Tstability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.
Paper's Title:
Coefficient Estimates for Certain Subclasses of Biunivalent Sakaguchi Type Functions by using Faber Polynomial
Author(s):
P. Murugabharathi, B. Srutha Keerthi
Mathematics Division,
School of Advanced Sciences,
VIT Chennai, Vandaloor, Kelambakkam Road,
Chennai  600 127, India.
Email: bharathi.muhi@gmail.com
Email: sruthilaya06@yahoo.co.in
Abstract:
In this work, considering a general subclass of biunivalent Sakaguchi type functions, we determine estimates for the general TaylorMaclaurin coefficients of the functions in these classes. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.
Paper's Title:
On Closed Range C^{*}modular Operators
Author(s):
Javad FarokhiOstad and Ali Reza Janfada
Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
Email: j.farokhi@birjand.ac.ir
ajanfada@birjand.ac.ir
Abstract:
In this paper, for the class of the modular operators on Hilbert C^{*}modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C^{*}modules are discussed. Moreover, the mixed reverse order law for the MoorePenrose invertible modular operators are given.
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:
A Generalization of Ostrowski's Inequality for Functions of Bounded Variation via a Parameter
Author(s):
Seth Kermausuor
Department of Mathematics and Computer
Science,
Alabama State University,
Montgomery, AL 36101,
USA.
Email:
skermausour@alasu.edu
Abstract:
In this paper, we provide a generalization of the Ostrowski's inequality for functions of bounded variation for k points via a parameter λ∈[0,1]. As a by product, we consider some particular cases to obtained some interesting inequalities in these directions. Our results generalizes some of the results by Dragomir in [S. S. DRAGOMIR, The Ostrowski inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999), pp. 495508.]
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:
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:
Optimal Control Analysis of HIV/AIDS Epidemic Model with an Antiretroviral Treatment
Author(s):
U. Habibah and R. A. Sari
Mathematics Department and Reseach Group
of Biomathematics,
Faculty of Mathematics and Natural Science,
Brawijaya University, Jl. Veteran Malang 65145,
Indonesia.
Email: ummu_habibah@ub.ac.id
Abstract:
A mathematical model of HIV/AIDS is governed by a system of ordinary differential equations in the presence of an antiretroviral treatment (ARV). The theory of optimal control is applied to an epidemic model of HIV/AIDS which an ARV is used as a control strategy in order to prevent the spread of HIV/AIDS. The optimality system is derived by applying the Pontryagin's Minimum Principle. We analyze the boundedness and positivity of solutions, and an existence of the optimal control. Numerical simulations are conducted to obtain numerical solution of the optimally system.
Paper's Title:
Inclusion Properties of a Certain Subclass of Strongly CloseToConvex Functions
Author(s):
S. M. Khairnar and M. More
Department of Mathematics,
Maharashtra Academy of Engineerring,
Alandi 412 105, Pune, Maharashtra,
INDIA.
smkhairnar2007@gmail.com,
meenamores@gmail.com.
Abstract:
The purpose of this paper is to derive some inclusion and argument properties of a new subclass of strongly closetoconvex functions in the open unit disc. We have considered an integral operator defined by convolution involving hypergeometric function in the subclass definition. The subclass also extends to the class of αspirallike functions of complex order.
Paper's Title:
Some Distortion and Other Properties Associated with a Family of the nFold Symmetric Koebe Type Functions
Author(s):
H. M. Srivastava, N. Tuneski and E. GeorgievaCelakoska
Department of Mathematics and Statistics,
University of Victoria,
Victoria, British Columbia V8W 3R4,
Canada
Faculty of Mechanical Engineering, St.
Cyril and Methodius University,
Karpo'v s II b.b., MK1000 Skopje,
Republic of Macedonia
Abstract:
In a recent work by Kamali and Srivastava [5], a certain family of the nfold symmetric Koebe type functions was introduced and studied systematically. In an earlier investigation, Eguchi and Owa [4] had considered its special case when n=1 (see also [10]). Here, in our present sequel to these earlier works, this general family of the nfold symmetric Koebe type functions is studied further and several distortion theorems and such other properties as the radii of spirallikeness, the radii of starlikeness and the radii of convexity, which are associated with this family of the nfold symmetric Koebe type functions, are obtained. We also provide certain criteria that embed this family of the nfold symmetric Koebe type functions in a function class G_{λ} which was introduced and studied earlier by Silverman [7].
Paper's Title:
Generalized Weighted Trapezoid and Grüss Type Inequalities on Time Scales
Author(s):
Eze Raymond Nwaeze
Department of Mathematics,
Tuskegee University,
Tuskegee, AL 36088,
USA.
Email: enwaeze@mytu.tuskegee.edu
Abstract:
In this work, we obtain some new generalized weighted trapezoid and Grüss type inequalities on time scales for parameter functions. Our results give a broader generalization of the results due to Pachpatte in [14]. In addition, the continuous and discrete cases are also considered from which, other results are obtained.
Paper's Title:
Some New Mappings Related to Weighted Mean Inequalities
Author(s):
XiuFen Ma
College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
Email: maxiufen86@163.com
Abstract:
In this paper, we define four mappings related to weighted mean inequalities, investigate their properties, and obtain some new refinements of weighted mean inequalities.
Paper's Title:
Applications of Von Neumann Algebras to Rigidity Problems of (2Step) Riemannian (Nil)Manifolds
Author(s):
Atefeh HasanZadeh and HamidReza Fanai
DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
Email: hasanzadeh.a@ut.ac.ir
Department of Mathematical Sciences,
Sharif University of Technology,
Iran
Email: fanai@sharif.edu
Abstract:
In this paper, basic notions of von Neumann algebra and its direct analogues in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric propositions of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic theorem of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2step nilmanifolds.
Paper's Title:
Fractional exp(φ(ξ)) Expansion Method and its Application to SpaceTime Nonlinear Fractional Equations
Author(s):
A. A. Moussa and L. A. Alhakim
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Alaamath81@gmail.com
URL:
https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Lama2736@gmail.com
URL:
https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar
Abstract:
In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the spacetime fractional nonlinear WhithamBroerKaup equations and spacetime fractional generalized nonlinear HirotaSatsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the reallife applications of the previous two equations will find this approach useful.
Paper's Title:
A Selfadaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces
Author(s):
F. U. Ogbuisi
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
Email: ferdinard.ogbuisi@unn.edu.ng
fudochukwu@yahoo.com
Abstract:
In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.
Paper's Title:
Bounds for the Extremal Eigenvalues of Positive Definite Matrices
Author(s):
Shivani Singh and Pravin Singh
Unisa, Department of Decision Sciences,
PO Box 392,
Pretoria,
0003,
South Africa.
Email: singhs2@unisa.ac.za
University of KwaZuluNatal,
School of Mathematics Statistics and Computer Sciences
Private Bag X54001,
Durban,
4000,
South Africa.
Email: singhprook@gmail.com
Abstract:
We use a projection to achieve bounds for a vector function of the eigenvalues of a positive definite matrix. For various choices of the monotonic function we are able to obtain bounds for the extremal eigenvalues in terms of the traces of the matrix and its powers. These bounds are relatively simple to compute.
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:
An alternative proof of monotonicity for the extended mean values
Author(s):
ChaoPing Chen and Feng Qi
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
chenchaoping@hpu.edu.cn
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
qifeng@hpu.edu.cn,
fengqi618@member.ams.org
Url:
http://rgmia.vu.edu.au/qi.html,
http://dami.hpu.edu.cn/qifeng.html
Abstract:
An alternative proof of monotonicity for the extended mean values is given.
Paper's Title:
A Wallis Type Inequality and a Double Inequality for Probability Integral
Author(s):
Jian Cao, DaWei Niu and Feng Qi
School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
21caojian@163.com
School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
nnddww@tom.com
Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng@hpu.edu.cn
fengqi618@member.ams.org
qifeng618@hotmail.com
qifeng618@msn.com
qifeng618@qq.com
URL: http://rgmia.vu.edu.au/qi.html
Abstract:
In this short note, a Wallis type inequality with the best upper and lower bounds is established. As an application, a double inequality for the probability integral is found.
Paper's Title:
A Different Proof for the nonExistence of HilbertSchmidt Hankel Operators with AntiHolomorphic Symbols on the Bergman Space
Author(s):
Georg Schneider
Universität Wien, Brünnerstr. 72 A1210 Wien,
Austria.
georg.schneider@univie.ac.at
URL: http://www.univie.ac.at/bwl/cont/mitarbeiter/schneider.htm
Abstract:
We show that there are no (nontrivial) HilbertSchmidt Hankel operators with antiholomorphic symbols on the Bergman space of the unitball B^{2}(B^{l}) for l≥2. The result dates back to [6]. However, we give a different proof. The methodology can be easily applied to other more general settings. Especially, as indicated in the section containing generalizations, the new methodology allows to prove some robustness results for existing ones.
Paper's Title:
The Invariant Subspace Problem for Linear Relations on Hilbert Spaces
Author(s):
Daniel GrixtiCheng
Department of Mathematics and Statistics,
The University of Melbourne,
Melbourne, VIC, 3010
Australia.
D.Grixti@ms.unimelb.edu.au
Abstract:
We consider the invariant subspace problem for linear relations on Hilbert spaces with the aim of promoting interest in the problem as viewed from the theory of linear relations. We present an equivalence between the single valued and multivalued invariant subspace problems and give some new theorems pertaining to the invariant subspace problem for linear relations on a Hilbert space.
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:
On Generalization of Hardytype Inequalities
Author(s):
K. Rauf, S. Ponnusamy and J. O. Omolehin
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
krauf@unilorin.edu.ng
Department of Mathematics,
Indian Institute of Technology Madras,
Chennai 600 036,
India
samy@iitm.ac.in
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
omolehin_joseph@yahoo.com
Abstract:
This paper is devoted to some new generalization of Hardytype integral inequalities and the reversed forms. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. Improvement of some inequalities are also presented.
Paper's Title:
Schwarz Method for Variational Inequalities Related to Ergodic Control Problems
Author(s):
S. Saadi, H. Mécheri
Department of Mathematics, Badji Mokhtar
University, Annaba 23000,
P.O.Box. 12, Annaba 23000, Algeria
Abstract:
In this paper, we study variational inequalities related to ergodic control problems studied by M. Boulbrachène and H. Sissaoui [11], where the "discount factor" (i.e., the zero order term) is set to 0, we use an overlapping Schwarz method on nomatching grid which consists in decomposing the domain in two subdomains. For α ∈ ]0.1[ we provide the discretization on each subdomain converges in L^{∞} norm.
Paper's Title:
New Refinements of Hölder's Inequality
Author(s):
XiuFen Ma
College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
Email: maxiufen86@163.com
Abstract:
In this paper, we define two mappings, investigate their properties, obtain some new refinements of Hölder's inequality.
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:
Convergence and Stability Results for New Three Step Iteration Process in Modular Spaces
Author(s):
Naresh Kumar and Renu Chugh
Department of Mathematics,
M.D. University,
Rohtak124001, Haryana,
India.
Email: nks280@gmail.com
Email: chugh.r1@gmail.com
Abstract:
The aim of this paper is to introduce a new iteration process (5) for ρcontraction mappings in Modular spaces. We obtain some analytical proof for convergence and stability of our iteration process (5). We show that our iteration process (5) gives faster convergence results than the leading AK iteration process (4) for contraction mappings. Moreover, a numerical example (using the Matlab Software) is presented to compare the rate of convergence for existing iteration processes with our new iteration process (5).
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:
Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces
Author(s):
^{1}U.A. Osisiogu, F.L. Adum, and ^{2}C. Izuchukwu
^{1}Department of Mathematics and
Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
Email: uosisiogu@gmail.com,
adumson2@yahoo.com
^{2}School of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: izuchukwuc@ukzn.ac.za,
izuchukwu_c@yahoo.com
Abstract:
The main purpose of this paper is to introduce a certain class of split generalized mixed equilibrium problem involving relaxed monotone mappings. To solve our proposed problem, we introduce an iterative algorithm and obtain its strong convergence to a solution of the split generalized mixed equilibrium problems in Hilbert spaces. As special cases of the proposed problem, we studied the proximal split feasibility problem and variational inclusion problem.
Paper's Title:
Action of Differential Operators On Chirpsconstruct On L^{∞}
Author(s):
Taoufik El Bouayachi and Naji Yebari
Laboratoire de Mathematiques et
applications,
Faculty of sciences and techniques, Tangier,
Morocco.
Email:
figo407@gmail.com,
yebarinaji@gmail.com
Abstract:
We will study in this work the action of differential operators on L∞ chirps and we will give a new definition of logarithmic chirp. Finally we will study the action of singular integral operators on chirps by wavelet characterization and Kernel method.
Paper's Title:
Analysis of the Dynamic Response of the Soilpile Behavioral Model Under Lateral Load
Author(s):
Ibrahima Mbaye, Mamadou Diop, Aliou Sonko and Malick Ba
University of Thies,
Department of Mathematics, Bp 967 Thies,
Senegal.
Email: imbaye@univthies.sn
mamadou.diop@univthies.sn
aliousonko59@gmail.com
mmalickba@hotmail.fr
URL: https://www.univthies.sn
Abstract:
This work aims to extend and improve our previous study on mathematical and numerical analysis of stationary Pasternak model. In this paper a dynamic response of Pasternak model is considered. On the one hand we establish the existence and uniqueness of the solution by using the LaxMilgram theorem and the spectral theory thus the existence of a Hilbert basis is shown and the spectral decomposition of any solution of the problem can be established and on the other hand the finite element method is used to determinate the numerical results. Furthermore, the influence of soil parameters G_{p} and K_{p} on the displacement of the pious is studied numerically at any time t_{n}.
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:
Lie Group Theoretic Approach of OneDimensional BlackScholes Equation
Author(s):
P. L. Zondi and M. B. Matadi
Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, KwaDlangezwa 3886,
South Africa.
Email: matadim@unizulu.ac.za
zondip@unizulu.ac.za
Abstract:
This study discusses the Lie Symmetry Analysis of BlackScholes equation via a modified local oneparameter transformations. It can be argued that the transformation of the BlackScholes equation is firstly obtained by means of riskless rate. Thereafter, the corresponding determining equations to the reduced equation are found. Furthermore, new symmetries of the BlackScholes equation are constructed and lead to invariant solutions.
Paper's Title:
A Caratheodory's Approximate Solutions of Stochastic Differential Equations Under the Hölder Condition
Author(s):
BoKyeong Kim and YoungHo Kim
Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnamdo 51140,
Korea.
Email: claire9576@naver.com
yhkim@changwon.ac.kr
Abstract:
In this paper, based on the theorem of the uniqueness of the solution of the stochastic differential equation, the convergence possibility of the Caratheodory's approximate solution was studied by approximating the unique solution. To obtain this convergence theorem, we used a Hölder condition and a weakened linear growth condition. Furthermore, The auxiliary theorems for the existence and continuity of the Caratheodory's approximate solution were investigated as a prerequisite.
Paper's Title:
Application of Chebyshev Polynomials to VolterraFredholm Integral Equations
Author(s):
Aissa Lakhal, Mostefa Nadir and Mohamed Nasseh Nadir
Department of Mathematics,
Faculty of Mathematics and
Informatics,
University of Msila,
Algeria.
Email:
aissa.lakhal@univmsila.dz
mostefa.nadir@univmsila.dz
nadir.mohamednasseh@yahoo.com
URL: https://www.mostefanadir.com
Abstract:
The goal of this work is to examine the numerical solution of linear VolterraFredholm integral equations of the second kind using the first, second, third and fourth Chebyshev polynomials. Noting that, the approximate solution is given in the form of series which converges to the exact one. Numerical examples are compared with other methods, in order to prove the applicability and the efficiency of this technical.
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