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24: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF 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 real-valued 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.



7: Paper Source PDF document

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 variational-like inequality problem and generalized vector equilibrium problem. The results of this paper generalize some known results in the literature.



6: Paper Source PDF document

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,
Phase-III, 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.



6: Paper Source PDF document

Paper's Title:

Generalizing Polyhedra to Infinite Dimension

Author(s):

Paolo d'Alessandro


Department of Mathematics, Third University of Rome,
Lgo S.L. Murialdo 1, 00146 Rome, Italy.


dalex@mat.uniroma3.it.


URL: http://www.mat.uniroma3.it/users/dalex/dalex.html.

Abstract:

This paper generalizes polyhedra to infinite dimensional Hilbert spaces as countable intersections of closed semispaces. Highlights are the structure theory that shows that a polyhedron is the sum of compact set (in a suitable topology) plus a closed pointed cone plus a closed subspace, giving the internal representation of polyhedra. In the final part the dual range space technique is extended to the solution of infinite dimensional LP problems.



5: Paper Source PDF document

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,
H-4010 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 2-homogeneous 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.



5: Paper Source PDF document

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 Saint-Etienne,

CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,

42023 Saint-Etienne Cedex 2, France.


 
rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional 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 thirty-one 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 thirty-one 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.



5: Paper Source PDF document

Paper's Title:

Expected Utility with Subjective Events

Author(s):

Jacob Gyntelberg and Frank Hansen

Bank for International Settlements,
Basel,
Switzerland

jacob.gyntelberg@bis.org


Tohoku University, Institute for International Education,
Sendai,
Japan

frank.hansen@m.tohoku.ac.jp

Abstract:

We provide a new theory of expected utility with subjective events modeled by a lattice of projections. This approach allows us to capture the notion of a ``small world'' as a context dependent or local state space embedded into a subjective set of events, the ``grand world''. For each situation the decision makers' subjective ``small world'' reflects the events perceived to be relevant for the act under consideration. The subjective set of events need not be representable by a classical state space. Maintaining preference axioms similar in spirit to the classical axioms, we obtain an expected utility representation which is consistent across local state spaces and separates subjective probability and utility. An added benefit is that this alternative expected utility representation allows for an intuitive distinction between risk and uncertainty.



5: Paper Source PDF document

Paper's Title:

Some Inequalities of the Hermite-Hadamard Type for k-Fractional Conformable Integrals

Author(s):

C.-J. Huang, G. Rahman, K. S. Nisar, A. Ghaffar and F. Qi

Department of Mathematics, Ganzhou Teachers College,
Ganzhou 341000, Jiangxi,
China.
E-mail: hcj73jx@126.com , huangcj1973@qq.com

Department of Mathematics, Shaheed Benazir Bhutto University,
Sheringal, Upper Dir, Khyber Pakhtoonkhwa,
Pakistan.
E-mail: gauhar55uom@gmail.com

Department of Mathematics, College of Arts and Science at Wadi Aldawaser, 11991,
Prince Sattam Bin Abdulaziz University, Riyadh Region,
Kingdom of Saudi Arabia.
E-mail: n.sooppy@psau.edu.sa, ksnisar1@gmail.com

Department of Mathematical Science, Balochistan University of Information Technology,
Engineering and Management Sciences, Quetta,
Pakistan.
E-mail: abdulghaffar.jaffar@gmail.com

School of Mathematical Sciences, Tianjin Polytechnic University,
Tianjin 300387,
China; Institute of Mathematics,
Henan Polytechnic University, Jiaozuo 454010, Henan,
China.
E-mail: qifeng618@gmail.com, qifeng618@qq.com

 

Abstract:

In the paper, the authors deal with generalized k-fractional conformable integrals, establish some inequalities of the Hermite-Hadamard type for generalized k-fractional conformable integrals for convex functions, and generalize known inequalities of the Hermite-Hadamard type for conformable fractional integrals.



4: Paper Source PDF document

Paper's Title:

Shape Diagrams for 2D Compact Sets - Part II: Analytic Simply Connected Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,

CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,

42023 Saint-Etienne Cedex 2, France.


 
rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact 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 twenty-two shape diagrams to be built. 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 twenty-two shape diagrams. The first part of this study is published in a previous paper 16. It focused 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 purpose of this paper is to present the second part, by focusing on analytic simply connected compact sets. The third part of the comparative study is published in a following paper 17. It is focused on convexity discrimination for analytic and discretized simply connected compact sets.



4: Paper Source PDF document

Paper's Title:

Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF 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 f-divergence 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 Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence 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.



4: Paper Source PDF document

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro1, Anca Croitoru2, Alina Gavriluţ2, Anna Rita Sambucini1

1Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

2Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.



3: Paper Source PDF document

Paper's Title:

On Stable Numerical Differentiation

Author(s):

N. S. Hoang and A. G. Ramm

Mathematics Department, Kansas State University
Manhattan, KS 66506-2602,
U. S. A.
nguyenhs@math.ksu.edu
ramm@math.ksu.edu
URL:http://math.ksu.edu/~ramm

Abstract:

Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete favorably with the variational regularization method for stable calculating the derivatives of noisy functions.



3: Paper Source PDF document

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 Brudnyi-Krugljak associated with the quasi-power 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 non-commutative symmetric spaces of measurable operators affiliated with a semi-finite von Neumann algebra.



3: Paper Source PDF document

Paper's Title:

Equivalence of the Nonsmooth Nonlinear Complementarity Problems to Unconstrained Minimization

Author(s):

M. A. Tawhid and J. L. Goffin

Department of Mathematics and Statistics, School of Advanced Technologies and Mathematics,
Thompson Rivers University,
900 McGill Road, PO Box 3010, Kamloops, BC V2C 5N3
Canada
Alexandria University and Egypt Japan University of Science and Technology,
Alexandria-Egypt
mtawhid@tru.ca  

Faculty of Management, McGill University,
1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5
Canada.
Jean-Louis.Goffin@McGill.ca 
 

Abstract:

This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the H-differentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe H-differentials of the associated penalized Fischer-Burmeister and Kanzow and Kleinmichel merit functions. We show how, under appropriate P0, semimonotone (E0), P, positive definite, and strictly semimonotone (E) -conditions on an H-differential of f, finding local/global minimum of a merit function (or a `stationary point' of a merit function) leads to a solution of the given nonlinear complementarity problem. Our results not only give new results but also unify/extend various similar results proved for C1.



3: Paper Source PDF document

Paper's Title:

On Generalization of Hardy-type 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 Hardy-type 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.



3: Paper Source PDF document

Paper's Title:

C*-valued metric projection and Moore-Penrose 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 35195-363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
E-mail: Madjid.Eshaghi@gmail.com

Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
E-mail: Hedayat.fathi@yahoo.com

Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
E-mail: shossein@uark.net

 

Abstract:

Let t be a regular operator between Hilbert C*-modules and t be its Moore-Penrose inverse. We give some characterizations for t based on C*-valued metric projection. Moore-Penrose inverse of bounded operators and elements of a C*-algebra is studied as a special case.



3: Paper Source PDF document

Paper's Title:

Some fixed point results in partial S-metric 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.
E-mail: Rezaee.mohammad.m@gmail.com

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: sedghi.gh@qaemiau.ac.ir

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: mukheimer@psu.edu.sa

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: kamal@psu.edu.sa

Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
E-mail: zoran.mitrovic@tdtu.edu.vn

Abstract:

We introduce in this article a new class of generalized metric spaces, called partial S-metric spaces. In addition, we also give some interesting results on fixed points in the partial S-metric spaces and some applications.



3: Paper Source PDF document

Paper's Title:

The Effect of Harvesting Activities on Prey-Predator 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.
E-mail: muh.nurulhuda@fmipa.unmul.ac.id
 fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id

Abstract:

This paper discussed prey-predator 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.



2: Paper Source PDF document

Paper's Title:

Long Time Behavior for a Viscoelastic Problem with a Positive Definite Kernel

Author(s):

Nasser-eddine Tatar

King Fahd University of Petroleum and Mineral, Department of Mathematical Sciences,
Dhahran, 31261 Saudi Arabia

tatarn@kfupm.edu.sa

Abstract:

We study the asymptotic behavior of solutions for an integro-differential problem which arises in the theory of viscoelasticity. It is proved that solutions go to rest in an exponential manner under new assumptions on the relaxation function in the memory term. In particular, we consider a new family of kernels which are not necessarily decreasing.



2: Paper Source PDF document

Paper's Title:

General Oscillations for Some Third Order Differential Systems with Nonlinear Acceleration Term

Author(s):

Awar Simon Ukpera

Department of Mathematics,
Obafemi Awolowo University,
Ile-Ife,
Nigeria.
aukpera@oauife.edu.ng

 

Abstract:

We generate some general nonuniform hypotheses for third order differential systems of the form X''' +F(t,X'' )+BX'+CX = P(t), in which B and C are not necessarily constant matrices. Some results requiring sharp conditions on this system have recently been published by the author in [5]. This work however examines more closely crucial properties associated with the generalised nature of the nonlinear acceleration term F, which were largely overlooked in the earlier paper.



2: Paper Source PDF document

Paper's Title:

A general theory of decision making

Author(s):

Frank Hansen

Department of Economics,
University of Copenhagen,
Studiestraede 6, DK-1455 Copenhagen K
Denmark Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh


Abstract:

We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of non-additive measures.



2: Paper Source PDF document

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 Diaz-Metcalf inequality with applications for complex polynomials is given.



2: Paper Source PDF document

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, Jan
áčkovo nám. 2a,
CZ-60200, 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.



2: Paper Source PDF document

Paper's Title:

Hyers-Ulam-Rassias Stability of a Generalized Jensen Functional Equation

Author(s):

A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani

Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr bbouikhalene@yahoo.fr

Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com Redouani-ahmed@yahoo.fr
 

Abstract:

In this paper we obtain the Hyers-Ulam-Rassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the Hyers-Ulam-stability of the K-spherical (n × n)-matrix functional equation.



2: Paper Source PDF document

Paper's Title:

Improvement of Jensen's Inequality for Superquadratic Functions

Author(s):

S. Abramovich, B. Ivanković, and J. Pečarić

Department of Mathematics,
University of Haifa,
Haifa 31905,
Israel.
abramos@math.haifa.ac.il

Faculty of Transport and Trafic Engineering,
University of Zagreb,
Vukelićeva 4, 10000,
Croatia
bozidar.ivankovic@zg.t-com.hr

Faculty of Textile,
University of Zagreb,
Prilaz Baruna Filipovića 30, 10000 Zagreb,
Croatia
pecaric@element.hr

 

Abstract:

Since 1907, the famous Jensen's inequality has been refined in different manners. In our paper, we refine it applying superquadratic functions and separations of domains for convex functions. There are convex functions which are not superquadratic and superquadratic functions which are not convex. For superquadratic functions which are not convex we get inequalities analogue to inequalities satisfied by convex functions. For superquadratic functions which are convex (including many useful functions) we get refinements of Jensen's inequality and its extensions.



2: Paper Source PDF document

Paper's Title:

Common Fixed Point Results for Banach Operator Pairs and Applications to Best Approximation

Author(s):

Hemant Kumar Nashine

Department of Mathematics,
Disha Institute of Management and Technology,
Satya Vihar, Vidhansabha - Chandrakhuri Marg (Baloda Bazar Road), Mandir Hasaud,
Raipur - 492101(Chhattisgarh), India.

hemantnashine@rediffmail.com
nashine_09@rediffmail.com
 

Abstract:

The common fixed point results for Banach operator pair with generalized nonexpansive mappings in q-normed space have been obtained in the present work. As application, some more general best approximation results have also been determined without the assumption of linearity or affinity of mappings. These results unify and generalize various existing known results with the aid of more general class of noncommuting mappings.



2: Paper Source PDF document

Paper's Title:

On Generalized Triangle Inequality in p-Freéchet Spaces, 0<p<1

Author(s):

M. A. Latif

Department of Mathematics,
University of Hail, Hail,
Saudi Arabia
m_amer_latif@hotmail.com

Abstract:

In this paper generalized triangle inequality and its reverse in a p-Fréchet space where, 0<p<1 are obtained.



2: Paper Source PDF document

Paper's Title:

A One-Line Derivation of the Euler and Ostrogradski Equations

Author(s):

Olivier de La Grandville

Stanford University,
Department of Management Science and Engineering,
Stanford, CA 94305,
U. S. A

ola@stanford.edu

Abstract:

At the very heart of major results of classical physics, the Euler and Ostrogradski equations have apparently no intuitive interpretation. In this paper we show that this is not so. Relying on Euler's initial geometric approach, we show that they can be obtained through a direct reasoning that does not imply any calculation. The intuitive approach we suggest offers two benefits: it gives immediate significance to these fundamental second-order non-linear differential equations; and second, it allows to obtain a property of the calculus of variations that does not seem to have been uncovered until now: the Euler and Ostrogradski equations can be derived not necessarily by giving a variation to the optimal function -- as is always done; one could equally well start by giving a variation to their derivative(s).



2: Paper Source PDF document

Paper's Title:

Hermite-Hadamard-Fejer Type Inequalities for Harmonically s-convex Functions via Fractional Integrals

Author(s):

İmdat İşcan, Mehmet Kunt

Department of Mathematics,
Faculty of Sciences and Arts,
Giresun University, Giresun,
Turkey.
E-mail: imdat.iscan@giresun.edu.tr


Department of Mathematics,
Faculty of Sciences,
Karadeniz Technical University,
61080, Trabzon,
Turkey.
E-mail: mkunt@ktu.edu.tr

Abstract:

In this paper, some Hermite-Hadamard-Fejer type integral inequalities for harmonically s-convex functions in fractional integral forms have been obtained.



2: Paper Source PDF document

Paper's Title:

On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations

Author(s):

Javad Izadi and Bahmann Yousefi

Department of Mathematics, Payame Noor University,
P.O. Box: 19395-3697, Tehran,
Iran.
E-mail: javadie2003@yahoo.com, b_yousefi@pnu.ac.ir

 

Abstract:

Let A be a Lie Banach*-algebra. For each elements (a, b) and (c, d) in A2:= A * A, by definitions

 (a, b) (c, d)= (ac, bd),
 |(a, b)|= |a|+ |b|,
(a, b)*= (a*, b*),

A2 can be considered as a Banach*-algebra. This Banach*-algebra is called a Lie Banach*-algebra whenever it is equipped with the following definitions of Lie product:

for all a, b, c, d in A. Also, if A is a Lie Banach*-algebra, then D: A2→A2 satisfying

 D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]

for all $a, b, c, d∈A, is a Lie derivation on A2. Furthermore, if A is a Lie Banach*-algebra, then D is called a Lie* derivation on A2 whenever D is a Lie derivation with D (a, b)*= D (a*, b*) for all a, b∈A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach*-algebra homomorphisms and Lie* derivations on the Banach*-algebra A2.



2: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for k-Riemann Liouville Fractional Integrals Via Two Kinds of Convexity

Author(s):

R. Hussain1, A. Ali2, G. Gulshan3, A. Latif4 and K. Rauf5

1,2,3,4Department of Mathematics,
Mirpur University of Science and Technology, Mirpur.
Pakistan.
E-mail1rashida12@gmail.com
E-mail2: unigraz2009@yahoo.com
E-mail3: ghazalagulshan@yahoo.com
E-mail4: asialatif87@gmail.com

5Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail5: krauf@unilorin.edu.ng

Abstract:

In this article, a fundamental integral identity including the first order derivative of a given function via k-Riemann-Liouville fractional integral is established. This is used to obtain further Hermite-Hadamard type inequalities involving left-sided and right-sided k-Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions respectively.



2: Paper Source PDF document

Paper's Title:

Weakly Compact Composition Operators on Real Lipschitz Spaces of Complex-valued Functions on Compact Metric Spaces with Lipschitz Involutions

Author(s):

D. Alimohammadi and H. Alihoseini

Department of Mathematics,
Faculty of Science, Arak University
P. O. Box,38156-8-8349, Arak,
Iran.
E-mail: d-alimohammadi@araku.ac.ir
E-mail: hr_alihoseini@yahoo.com
URL: http://www.araku.ac.ir

Abstract:

We first show that a bounded linear operator T on a real Banach space E is weakly compact if and only if the complex linear operator T on the complex Banach space EC is weakly compact, where EC is a suitable complexification of E and iT' is the complex linear operator on EC associated with T. Next we show that every weakly compact composition operator on real Lipschitz spaces of complex-valued functions on compact metric spaces with Lipschitz involutions is compact.



2: Paper Source PDF document

Paper's Title:

On Closed Range C*-modular Operators

Author(s):

Javad Farokhi-Ostad and Ali Reza Janfada

Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
E-mail: 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 Moore-Penrose invertible modular operators are given.



2: Paper Source PDF document

Paper's Title:

A New Adomian Approach to Solving Integral Equations of Fredholm and Volterra Second Kind

Author(s):

Ouedraogo Seny, Nebie Abdoul Wassiha, Youssouf Pare, Blaise Some

Departement de mathematiques,
Universite Joseph Ki-Zerbo,
Burkina Faso.
E-mail: oseny@yahoo.fr, nebwass@yahoo.fr
pareyoussouf@yahoo.fr, some@univ-ouaga.bf

Abstract:

In order to simplify the resolution of Fredholm and Volterra's second type integral equations, we propose a new approach based on the Adomian Decompositional Method (ADM). We test the new approach on several examples with success.



2: Paper Source PDF document

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, Coimbatore-10, Tamilnadu,
India.
E-mail: parvathasathish@gmail.com

Post Graduate and Research Department of Mathematics,
Govt. Arts College, Coimbatore-641018, Tamilnadu,
India.
E-mail: 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  T2  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.



2: Paper Source PDF document

Paper's Title:

Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF 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: https://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



2: Paper Source PDF document

Paper's Title:

Attempts to Define a Baum--Connes Map Via Localization of Categories for Inverse Semigroups

Author(s):

Bernhard Burgstaller

Departamento de Matematica,
Universidade Federal de Santa Catarina,
CEP 88.040-900 Florianopolis-SC,
Brasil.
E-mail: bernhardburgstaller@yahoo.de
URL: http://mathematik.work/bernhardburgstaller/index.html

Abstract:

An induction functor in inverse semigroup equivariant KK-theory is considered, and together with %a restriction functors certain results similar to those known from the Mackey machinery are shown. It is also verified that for any so-called E-continuous inverse semigroup its equivariant KK-theory satisfies the universal property and is a triangulated category.



2: Paper Source PDF document

Paper's Title:

On Subspace-Supercyclic Operators

Author(s):

Mansooreh Moosapoor

Assistant Professor,
Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: mosapor110@gmail.com m.mosapour@cfu.ac.ir

Abstract:

In this paper, we prove that supercyclic operators are subspace-supercyclic and by this we give a positive answer to a question posed in ( L. Zhang, Z. H. Zhou, Notes about subspace-supercyclic operators, Ann. Funct. Anal., 6 (2015), pp. 60--68). We give examples of subspace-supercyclic operators that are not subspace-hypercyclic. We state that if T is an invertible supercyclic operator then Tn and T-n is subspace-supercyclic for any positive integer n. We give two subspace-supercyclicity criteria. Surprisingly, we show that subspace-supercyclic operators exist on finite-dimensional spaces.



2: Paper Source PDF document

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.
E-mail: 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.



2: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for MN-Convex Functions

Author(s):

Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF 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: https://rgmia.org/dragomir 

Abstract:

The present work endeavours to briefly present some of the fundamental results connected to the Hermite-Hadamard inequality for special classes of convex functions such as AG, AH, GA, GG, GH, HA, HG and HH -convex functions in which the author have been involved during the last five years. For simplicity, we call these classes of functions such as MN-convex functions, where M and N stand for any of the Arithmetic (A), Geometric (G) or Harmonic (H) weighted means of positive real numbers. The survey is intended for use by both researchers in various fields of Approximation Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



1: Paper Source PDF document

Paper's Title:

Integrability of Sine and Cosine Series Having Coefficients of a New Class

Author(s):

L. Leindler

Bolyai Institute, University of Szeged, Aradi Vértanúk Tere 1, H-6720 Szeged, Hungary
leindler@math.u-szeged.hu

Abstract:

Some integrability theorems or only their sufficient part are generalized such that the coefficients of the sine and cosine series belong to a new class of sequences being wider than the class of sequences of rest bounded variation, which itself is a generalization of the monotone decreasing sequences, but a subclass of the almost monotone decreasing sequences. It is also verified that the new class of sequences and the class of almost monotone decreasing sequences are not comparable.



1: Paper Source PDF document

Paper's Title:

An Algorithm to Compute Gaussian-Type 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@univ-pau.fr
URL: http://www.univ-pau.fr/~aguessab/

Abstract:

It is well-known 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.



1: Paper Source PDF document

Paper's Title:

Positive Solutions of Evolution Operator Equations

Author(s):

Radu Precup

Department of Applied Mathematics,
Babes-Bolyai University,
Cluj, Romania

Abstract:

Existence and localization results are derived from Krasnoselskii’s compressionexpansion fixed point theorem in cones, for operator equations in spaces of continuous functions from a compact real interval to an abstract space. The main idea, first used in [12], is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskii’s theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. An application is presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain.



1: Paper Source PDF document

Paper's Title:

Ellipses of Maximal Area and of Minimal Eccentricity Inscribed in a Convex Quadrilateral

Author(s):

Alan Horwitz

Penn State University,
25 Yearsley Mill Rd., Media, Pa 19063
alh4@psu.edu 
Url: www.math.psu.edu/horwitz

Abstract:

Let Ð be a convex quadrilateral in the plane and let M1 and M2 be the midpoints of the diagonals of Ð. It is well–known that if E is an ellipse inscribed in Ð, then the center of E must lie on Z, the open line segment connecting M1 and M2 . We use a theorem of Marden relating the foci of an ellipse tangent to the lines thru the sides of a triangle and the zeros of a partial fraction expansion to prove the converse: If P lies on Z, then there is a unique ellipse with center P inscribed in Ð. This completely characterizes the locus of centers of ellipses inscribed in Ð. We also show that there is a unique ellipse of maximal area inscribed in Ð. Finally, we prove our most signifigant results: There is a unique ellipse of minimal eccentricity inscribed in Ð.



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Paper's Title:

Some Approximation for the linear combinations of modified Beta operators

Author(s):

Naokant Deo

Department of Applied Mathematics
Delhi College of Engineering
Bawana Road, Delhi - 110042,
India.
dr_naokant_deo@yahoo.com


Abstract:

In this paper, we propose a sequence of new positive linear operators βn to study the ordinary approximation of unbounded functions by using some properties of the Steklov means.



1: Paper Source PDF document

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.



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Paper's Title:

Note on the Rank of Birkhoff Interpolation

Author(s):

J. Rubió-Massegú

Applied Mathematics III, Universitat Politècnica de Catalunya,
Colom 1, 08222, Terrassa,
Spain
josep.rubio@upc.edu


Abstract:

The relationship between a variant of the rank of a univariate Birkhoff interpolation problem, called normal rank, and other numbers of interest associated to the interpolation problem is studied.



1: Paper Source PDF document

Paper's Title:

Coincidences and Fixed Points of Hybrid Maps in Symmetric Spaces

Author(s):

S. L. Singh and Bhagwati Prasad

Vedic MRI, 21 Govind Nagar,
Rishikesh 249201
India
vedicmri@gmail.com

Department of Mathematics, Gurukula Kangri University,
Hardwar 249404,
India


Abstract:

The purpose of this paper is to obtain a new coincidence theorem for a single-valued and two multivalued operators in symmetric spaces. We derive fixed point theorems and discuss some special cases and applications.



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Paper's Title:

Generalizations of Hermite-Hadamard's Inequalities for Log-Convex Functions

Author(s):

Ai-Jun Li

School of Mathematics and Informatics, Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com


Abstract:

In this article, Hermite-Hadamard's inequalities are extended in terms of the weighted power mean and log-convex function. Several refinements, generalizations and related inequalities are obtained.



1: Paper Source PDF document

Paper's Title:

Existence of Bounded Solutions for a Class of Strongly Nonlinear Elliptic Equations in Orlicz-Sobolev Spaces

Author(s):

Abdelmoujib Benkirane and Ahmed Youssfi

Department of Mathematics and Informatics, Faculty of Sciences Dhar El Mahraz
University Sidi Mohammed Ben Abdallah
PB 1796 Fez-Atlas, Fez
Morocco
a.benkirane@menara.ma
ahmed.youssfi@caramail.com


Abstract:

We prove, in the setting of Orlicz-Sobolev spaces, the existence of bounded solutions for some strongly nonlinear elliptic equations with operator of the principal part having degenerate coercivity and lower order terms not satisfying the sign condition. The data have a suitable summability and no Δ2-condition is needed for the considered N-functions.



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Paper's Title:

Differentiability of Distance Functions in p-Normed Spaces

Author(s):

M. S. Moslehian, A. Niknam, S. Shadkam Torbati

Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS),,
 Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad,
Iran

moslehian@ferdowsi.um.ac.ir
niknam@math.um.ac.ir
shadkam.s@wali.um.ac.ir

Abstract:

The farthest point mapping in a p-normed space X is studied in virtue of the Gateaux derivative and the Frechet derivative. Let M be a closed bounded subset of X having the uniformly p-Gateaux differentiable norm. Under certain conditions, it is shown that every maximizing sequence is convergent, moreover, if M is a uniquely remotal set then the farthest point mapping is continuous and so M is singleton. In addition, a Hahn--Banach type theorem in $p$-normed spaces is proved.



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Paper's Title:

Stability of Almost Multiplicative Functionals

Author(s):

Norio Niwa, Hirokazu Oka, Takeshi Miura and Sin-Ei Takahasi

Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa 572-8530,
Japan

Faculty of Engineering, Ibaraki University,
Hitachi 316-8511,
Japan

Department of Applied Mathematics and Physics, Graduate School of Science and Engineering,
Yamagata University,
Yonezawa 992-8510
Japan

oka@mx.ibaraki.ac.jp
miura@yz.yamagata-u.ac.jp
sin-ei@emperor.yz.yamagata-u.ac.jp

Abstract:

Let δ and p be non-negative real numbers. Let be the real or complex number field and a normed algebra over . If a mapping satisfies

then we show that φ is multiplicative or for all If, in addition, φ satisfies

for some p1, then by using Hyers-Ulam-Rassias stability of additive Cauchy equation, we show that φ is a ring homomorphism or for all In other words, φ is a ring homomorphism, or an approximately zero mapping. The results of this paper are inspired by Th.M. Rassias' stability theorem.



1: Paper Source PDF document

Paper's Title:

On Some Mapping Properties of Möbius Transformations

Author(s):

Nihal Yilmaz Özgür

Balkesir University, Faculty of Arts and Sciences, Department of Mathematics,
10145 Balkesir,
TURKEY
nihal@balikesir.edu.tr
URL
: http://w3.balikesir.edu.tr/~nihal/

Abstract:

We consider spheres corresponding to any norm function on the complex plane and their images under the Möbius transformations. We see that the sphere preserving property is not an invariant characteristic property of Möbius transformations except in the Euclidean case.



1: Paper Source PDF document

Paper's Title:

Hyperbolic Barycentric Coordinates

Author(s):

Abraham A. Ungar

Department of Mathematics, North Dakota State University,
Fargo, ND 58105,
USA
Abraham.Ungar@ndsu.edu
URL
: http://math.ndsu.nodak.edu/faculty/ungar/

Abstract:

A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.



1: Paper Source PDF document

Paper's Title:

On the product of M-measures in l-groups

Author(s):

A. Boccuto, B. Riěcan, and A. R. Sambucini

Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I-06123 Perugia,
Italy.
 boccuto@dipmat.unipg.it
 URL: http://www.dipmat.unipg.it/~boccuto


 Katedra Matematiky, Fakulta Prírodných Vied,
Univerzita Mateja Bela,
Tajovského, 40, Sk-97401 Banská Bystrica,
Slovakia.
 riecan@fpv.umb.sk


 Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I-06123 Perugia,
Italy.
 matears1@unipg.it
 URL: http://www.unipg.it/~matears1

 

Abstract:

Some extension-type theorems and compactness properties for the
product of l-group-valued M-measures are proved.



1: Paper Source PDF document

Paper's Title:

The Riemann-Stieltjes Integral on Time Scales

Author(s):

D. Mozyrska, E. Pawłuszewicz, D. Torres

Faculty Of Computer Science,
Białystok University Of Technology,
15-351 Białystok,
 Poland
 d.mozyrska@pb.edu.pl


 Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
 ewa@ua.pt


 Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
 delfim@ua.pt

 

Abstract:

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given



1: Paper Source PDF document

Paper's Title:

Approximation of Derivatives in a Singularly Perturbed Second Order Ordinary Differential Equation with Discontinuous Terms Arising in Chemical Reactor Theory

Author(s):

R. Mythili Priyadharshini and N. Ramanujam

Department of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, India.
matram2k3@yahoo.com
URL: http://www.bdu.ac.in/depa/science/ramanujam.htm

Abstract:

In this paper, a singularly perturbed second order ordinary differential equation with a discontinuous convection coefficient arising in chemical reactor theory is considered. A robust-layer-resolving numerical method is suggested. An ε-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.



1: Paper Source PDF document

Paper's Title:

Uniqueness of Meromorphic Functions and Weighted Sharing

Author(s):

Indrajit Lahiri and Rupa Pal

Department of Mathematics, University of
Kalyani, West Bengal 741235, India

indr9431@dataone.in


 Jhargram Raj College,
Jhargram, Midnapur(W),
West Bengal 721507,
India
rupa.a.pal@gmail.com

Abstract:

With the help of the notion of weighted sharing of values, we prove a result on uniqueness of meromorphic functions and as a consequence we improve a result of P. Li



1: Paper Source PDF document

Paper's Title:

Two Remarks on Commutators of Hardy Operator

Author(s):

Yasuo Komori-Furuya

School of High Technology for Human Welfare 
Tokai University
317 Nishino Numazu, Shizuoka 410-0395 Japan
komori@wing.ncc.u-tokai.ac.jp  

Abstract:

Fu and Lu showed that
the commutator of multiplication operator by b and
the n-dimensional Hardy operator
is bounded on Lp if b is in some CMO space.
We shall prove the converse of this theorem
and also prove that their result is optimal by giving a counterexample



1: Paper Source PDF document

Paper's Title:

On an Elliptic Over-Determined 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.

lragoub@yu.edu.sa

 

Abstract:

We extend the method of Weinberger for a non-linear over-determined elliptic problem
in R2. We prove that the domain in consideration is a ball. The tool of this investigation are maximum principles and P-functions.



1: Paper Source PDF document

Paper's Title:

Uniform Convergence of Schwarz Method for Noncoercive Variational Inequalities Simple Proof

Author(s):

M. Haiour and E. Hadidi.


Department of mathematics, LANOS Laboratory,
Faculty of the Sciences, University Badji Mokhtar,
P.O 23000 Annaba,
Algeria.


haiourm@yahoo.fr,
ehadidi71@yahoo.fr

Abstract:

In this paper we study noncoercive variational inequalities, using the Schwarz method. The main idea of this method consists in decomposing the domain in two subdomains. We give a simple proof for the main result concerning L error estimates, using the Zhou geometrical convergence and the L approximation given for finite element methods by Courty-Dumont.  



1: Paper Source PDF document

Paper's Title:

Sharp Lp Improving Results for Singular Measures on Cn+1

Author(s):

E. Ferreyra, M. Urciuolo

FaMAF-CIEM,
Universidad Nacional de Córdoba-Conicet,
Ciudad Universitaria, 5000 Córdoba,
Argentina

eferrey@famaf.unc.edu.ar
urciuolo@famaf.unc.edu.ar

Abstract:

For j=1,...,n, let Ωj be open sets of the complex plane and let φj be holomorphic functions on Ωj such that φj'' does not vanish identically on Ωj. We consider φ(z1,...,zn) =φ1(z1) +...+φn(zn). We characterize the pairs (p,q) such that the convolution operator with the surface measure supported on a compact subset of the graph of φ is p-q bounded.



1: Paper Source PDF document

Paper's Title:

Para-chaotic Tuples of Operators

Author(s):

Bahmann Yousefi and Javad Izadi

Department of Mathematics,
Payame Noor University,
P.O. Box 19395-3697, Tehran,
Iran
b_yousefi@pnu.ac.ir
javadie2003@yahoo.com

Abstract:

In this paper, we introduce para-chaotic tuples of operators and we give some relations between para-chaoticity and Hypercyclicity Criterion for a tuple of operators.



1: Paper Source PDF document

Paper's Title:

Multilinear Fractional Integral Operators on Herz Spaces

Author(s):

Yasuo Komori-Furuya

School of High Technology and Human Welfare,
Tokai University, 317 Nishino Numazu Shizuoka, 410-0395
Japan

komori@wing.ncc.u-tokai.ac.jp

Abstract:

We prove the boundedness of the multilinear fractional integral operators of Kenig and Stein type on Herz spaces. We also show that our results are optimal.



1: Paper Source PDF document

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

signor_2000@yahoo.fr

Mcherihalima@yahoo.fr

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.



1: Paper Source PDF document

Paper's Title:

An Improvement of the Hermite-Hadamard Inequality for Functions Convex on the Coordinates

Author(s):

Milica Klaričić Bakula

Faculty of Science,
University of Split,
Teslina 12, 21000 Split.
Croatia

E-mail: milica@pmfst.hr

Abstract:

An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates is given.



1: Paper Source PDF document

Paper's Title:

L∞- Error Estimate of Schwarz Algorithm for Elliptic Quasi-Variational Inequalities Related to Impulse Control Problem

Author(s):

Saadi Samira and Mehri Allaoua

Lab. LANOS, Department of Mathematics,
University Badji Mokhtar Annaba,
P.O.Box 12, Annaba 23000,
Algeria.

Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.

E-mail: saadisamira69@yahoo.fr
allmehri@yahoo.fr

Abstract:

In this work, we study Schwarz method for a class of elliptic quasi-variational inequalities. The principal result of this investigation is to prove the error estimate in ∞-norm for two domains with overlapping nonmatching grids, using the geometrical convergence, and the uniform convergence of Cortey Dumont.



1: Paper Source PDF document

Paper's Title:

New Stochastic Calculus

Author(s):

Moawia Alghalith

Department of Economics,
University of the West Indies, St. Augustine,
Trinidad and Tobago.

E-mail: malghalith@gmail.com
 

Abstract:

We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.



1: Paper Source PDF document

Paper's Title:

Optimization and Approximation for Polyhedra in Separable Hilbert Spaces

Author(s):

Paolo d'Alessandro

Department of Mathematics,
Third University of Rome,
Italy.

E-mail: pdalex45@gmail.com

Abstract:

This paper studies infinite dimensional polyhedra, covering the case in which range spaces of operators defining inequality systems are not closed. A rangespace method of linear programming is generalized to infinite dimensions and finite dimensional methods of approximation are introduced.



1: Paper Source PDF document

Paper's Title:

Ostrowski Type Fractional Integral Inequalities for Generalized (s,m,φ)-preinvex Functions

Author(s):

Artion Kashuri and Rozana Liko

University of Vlora "Ismail Qemali",
Faculty of Technical Science,
Department of Mathematics, 9400,
Albania.
E-mail: artionkashuri@gmail.com
E-mail: rozanaliko86@gmail.com

Abstract:

In the present paper, the notion of generalized (s,m,φ)-preinvex function is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (s,m,φ)-preinvex functions along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for generalized (s,m,φ)-preinvex functions via Riemann-Liouville fractional integrals are established.



1: Paper Source PDF document

Paper's Title:

On The Rayleigh-Love Rod Accreting In Both Length And Cross-Sectional Area: Forced And Damped Vibrations

Author(s):

M.L.G. Lekalakala1, M. Shatalov2, I. Fedotov3, S.V. Joubert4

1Department of Mathematics, Vaal University of Technology, P.O. Box 1889, Secunda, 2302, South Africa.
E-mail1: glen@vut.ac.za 

2,3,4Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa.

Abstract:

In this paper an elastic cylindrical rod that is subjected to forced and damped vibrations is considered. The rod is assumed to be isotropic. The applied external force of excitation is assumed to be harmonic, and the damping force is that of Kelvin-Voigt. The longitudinally vibrating rod is fixed at the left end and free at the other end. The rod is assumed to be accreting in length and cross-sectional area as it vibrates. The problem arising and the dynamics of the vibrating rod are described and investigated within the Rayleigh-Love theories of the rod. A partial differential equation describing the longitudinal displacement of the rod is formulated. The formulated partial differential equation, together with the corresponding boundary conditions as per the configuration of the rod, is solved numerically using the Galerkin-Kantorovich method. The frequency of vibration of the harmonic exciting force is kept constant in this investigation.

It is shown that in this periodically forced viscoelastic damped vibration, all the modes of vibration are subjected to the resonance behaviour within a proper time interval, depending on the length of the accreting rod.



1: Paper Source PDF document

Paper's Title:

Birkhoff-James orthogonality and Best Approximant in L1(X)

Author(s):

Mecheri Hacene and Rebiai Belgacem

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: mecherih2000@yahoo.fr

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: brebiai@gmail.com

Abstract:

Let X  be a complex Banach space and let (X,ρ) be a positive measure space. The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of Birkhoff-James orthogonality of bounded linear operators in L1(X,ρ) also implies best approximation has been proved.



1: Paper Source PDF document

Paper's Title:

Some Convergence Results for  Jungck-Am Iterative Process In Hyperbolic Spaces

Author(s):

Akindele Adebayo Mebawondu and Oluwatosin Temitope Mewomo

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216028272@stu.ukzn.ac.za, mewomoo@ukzn.ac.za

Abstract:

In this paper, we introduce a new three steps iterative process called Jungck-AM iterative process and show that the proposed iterative process can be used to approximate fixed points of Jungck-contractive type mappings and Jungck-Suzuki type mappings. In addition, we establish some strong and Δ-convergence results for the approximation of fixed points of Jungck-Suzuki type mappings in the frame work of uniformly convex hyperbolic space. Furthermore, we show that the newly proposed iterative process has a better rate of convergence compare to the Jungck-Noor, Jungck-SP, Jungck-CR and some existing iterative processes in the literature. Finally, stability, data dependency results for Jungck-AM iterative process is established and we present an analytical proof and numerical examples to validate our claim.



1: Paper Source PDF document

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.
E-mail: 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.



1: Paper Source PDF document

Paper's Title:

A new approach to the study of fixed point for simulation functions with application in G-metric spaces

Author(s):

Komi Afassinou and Ojen Kumar Narain

Department of Mathematical Sciences, University of Zululand,
KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)-Z-contraction mapping, Suzuki generalized (α,β)-Z-contraction mapping, (α,β)-admissible mapping and triangular (α,β)-admissible mapping in the frame work of G-metric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete G-metric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.



1: Paper Source PDF document

Paper's Title:

Applications of Von Neumann Algebras to Rigidity Problems of (2-Step) Riemannian (Nil-)Manifolds

Author(s):

Atefeh Hasan-Zadeh and Hamid-Reza Fanai

DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
E-mail: hasanzadeh.a@ut.ac.ir

Department of Mathematical Sciences,
Sharif University of Technology,
Iran
E-mail: 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 2-step nilmanifolds.



1: Paper Source PDF document

Paper's Title:

Composite Variational-Like Inequalities Given By Weakly Relaxed ζ-Semi-Pseudomonotone Multi-Valued Mapping

Author(s):

Syed Shakaib Irfan, Iqbal Ahmad, Zubair Khan and Preeti Shukla

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: shakaib@qec.edu.sa

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: zkhan@iul.ac.in

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: shuklapreeti1991@gmail.com

 

Abstract:

In this article, we introduce a composite variational-like inequalities with weakly relaxed ζ-pseudomonotone multi-valued maping in reflexive Banach spaces. We obtain existence of solutions to the composite variational-like inequalities with weakly relaxed ζ-pseudomon -otone multi-valued maps in reflexive Banach spaces by using KKM theorem. We have also checked the solvability of the composite variational-like inequalities with weakly relaxed ζ-semi-pseudomonotone multi-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.



1: Paper Source PDF document

Paper's Title:

A Self-adaptive 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 KwaZulu-Natal, Durban,
South Africa.

Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: 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 2-uniformly 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 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.



1: Paper Source PDF document

Paper's Title:

ψ(m,q)-Isometric Mappings on Metric Spaces

Author(s):

Sid Ahmed Ould Beinane, Sidi Hamidou Jah and Sid Ahmed Ould Ahmed Mahmoud

Mathematical Analysis and Applications, Mathematics Department, College of Science,
Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: beinane06@gmail.com

Department of Mathematics, College of Science Qassim University,
P.O. Box 6640, Buraydah 51452,
Saudi Arabia.
E-mail: jahsiidi@yahoo.fr

Mathematical Analysis and Applications,
Mathematics Department, College of Science, Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: sidahmed@ju.edu.sa, sidahmed.sidha@gmail.com

Abstract:

The concept of (m,p)-isometric operators on Banach space was extended to (m,q)-isometric mappings on general metric spaces in [6]. This paper is devoted to define the concept of ψ(m, q)-isometric, which is the extension of A(m, p)-isometric operators on Banach spaces introduced in [10]. Let T,ψ: (E,d) -> (E, d) be two mappings.
For some positive integer m and q (0,). T is said to be an ψ(m,q)-isometry, if for all  y,z E,



1: Paper Source PDF document

Paper's Title:

Existence and Approximation of Traveling Wavefronts for the Diffusive Mackey-Glass Equation

Author(s):

C. Ramirez-Carrasco and J. Molina-Garay

Facultad de Ciencias Basicas,
Universidad Catolica del Maule, Talca,
Chile
E-mail: carloshrc1989@gmail.com
 molina@imca.edu.pe

Abstract:

In this paper, we consider the diffusive Mackey-Glass 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 upper-lower solutions. Finally, through an iterative procedure, we show numerical simulations that approximate the traveling wavefronts, thus confirming our theoretical results.


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