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5: Paper Source PDF document

Paper's Title:

On A Conjecture of A Logarithmically Completely Monotonic Function

Author(s):

Valmir Krasniqi, Armend Sh. Shabani

Department of Mathematics,
University of Prishtina,
Republic of Kosova

E-mail: vali.99@hotmail.com  
armend_shabani@hotmail.com

Abstract:

In this short note we prove a conjecture, related to a logarithmically completely monotonic function, presented in [5]. Then, we extend by proving a more generalized theorem. At the end we pose an open problem on a logarithmically completely monotonic function involving q-Digamma function.



3: Paper Source PDF document

Paper's Title:

Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

M. Lakrib, A. Oumansour and K. Yadi  

Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz

Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz

Abstract:

In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.



3: Paper Source PDF document

Paper's Title:

Some interesting properties of finite continuous Cesàro operators

Author(s):

Abdelouahab Mansour and Abderrazak Hechifa

Operator theory laboratory (LABTHOP),
Eloued University,
Algeria.
E-mail: amansour@math.univ-lyon1.fr

Mathematics Department,
Faculty of Science,
Badji Mokhtar University, -Annaba,
Algeria.
E-mail: abderrazak02@gmail.com

Abstract:

A complex scalar λ is called an extended eigenvalue of a bounded linear operator T on a complex Banach space if there is a nonzero operator X such that TX = λ XT, the operator X is called extended eigenoperator of T corresponding to the extended eigenvalue λ.

In this paper we prove some properties of extended eigenvalue and extended eigenoperator for C1 on Lp([0,1]), where C1 is the Cesàro operator defined on the complex Banach spaces Lp([0 , 1])  for 1<p<∞ by the expression



2: Paper Source PDF document

Paper's Title:

On Oscillation of Second-Order Delay Dynamic Equations on Time Scales

Author(s):

S. H. Saker

Department of Mathematics, Faculty of Science,
Mansoura University, Mansoura, 35516,
Egypt.
shsaker@mans.edu.eg


Abstract:

Some new oscillation criteria for second-order linear delay dynamic equation on a time scale T are established. Our results improve the recent results for delay dynamic equations and in the special case when T=R, the results include the oscillation results established by Hille [1948, Trans. Amer. Math. Soc. 64 (1948), 234-252] and Erbe [Canad. Math. Bull. 16 (1973), 49-56.] for differential equations. When T=Z the results include and improve some oscillation criteria for difference equations. When T=hZ, h>0, T=qN and T=N2, i.e., for generalized second order delay difference equations our results are essentially new and can be applied on different types of time scales. An example is considered to illustrate the main results.



2: Paper Source PDF document

Paper's Title:

Topological Aspects of Scalarization in Vector Optimization Problems.

Author(s):

Peter I. Kogut, Rosanna Manzo and Igor V. Nechay

Department of Differential Equations,
Dnipropetrovsk National University, Naukova STR.,
 13, 49010 Dnipropetrovsk,
Ukraine
 
p.kogut@i.ua

Università di Salerno,
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata,
Via Ponte don Melillo, 84084 Fisciano (SA),
Italy
 
manzo@diima.unisa.it

Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan STR., 2, 49010 Dnipropetrovsk,
Ukraine
 
i.nechay@i.ua

Abstract:

In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vector-valued mappings with a weakened property of lower semicontinuity. We also prove the existence of the so-called generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.



1: Paper Source PDF document

Paper's Title:

On Perturbed Reflection Coefficients

Author(s):

J. L. Díaz-Barrero and J. J. Egozcue

Applied Mathematics III,
Universidad Politécnica de Cataluña,
Barcelona, Spain
jose.luis.diaz@upc.edu
juan.jose.egozcue@upc.edu


Abstract:

Many control and signal processing applications require testing stability of polynomials. Classical tests for locating zeros of polynomials are recursive, but they must be stopped whenever the so called "singular polynomials" appear. These ``singular cases'' are often avoided by perturbing the "singular polynomial". Perturbation techniques although always successful are not proven to be well-founded. Our aim is to give a mathematical foundation to a perturbation method in order to overcome "singular cases" when using Levinson recursion as a testing method. The non-singular polynomials are proven to be dense in the set of all polynomials respect the L²-norm on the unit circle . The proof is constructive and can be used algorithmically.



1: Paper Source PDF document

Paper's Title:

On a Subclass of Uniformly Convex Functions Defined by the Dziok-Srivastava Operator

Author(s):

M. K. Aouf and G. Murugusundaramoorthy

Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

School of Science and Humanities, VIT University
Vellore - 632014,
India.
gmsmoorthy@yahoo.com


Abstract:

Making use of the Dziok-Srivastava operator, we define a new subclass Tlm([α1];α,β) of uniformly convex function with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of close-to-convexity, starlikeness and convexity for functions belonging to the class Tlm([α1];α,β) . We consider integral operators associated with functions belonging to the class Hlm([α1];α,β) defined via the Dziok-Srivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class Tlm([α1];α,β) and we obtain properties associated with generalized fractional calculus operators.



1: Paper Source PDF document

Paper's Title:

A Subclass of Meromorphically Multivalent Functions with Applications to Generalized Hypergeometric Functions

Author(s):

M. K. Aouf

Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt
mkaouf127@yahoo.com

Abstract:

In this paper a new subclass of meromorphically multivalent functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically p-valent functions. The main object of the present paper is to investigate the various important properties and characteristics of this subclass of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to this subclass. Also we consider several applications of our main results to generalized hypergeomtric functions.



1: Paper Source PDF document

Paper's Title:

Inclusion and Neighborhood Properties for Certain Subclasses of Analytic Functions Associated with Convolution Structure

Author(s):

M. K. Aouf

Mathematics Department,
Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

Abstract:

In this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order defined by using the familiar convolution structure of analytic functions. In this paper we obtain the coefficient estimates and the consequent inclusion relationships involving the neighborhoods of the p-valently analytic functions.



1: Paper Source PDF document

Paper's Title:

Generalized Efficient Solutions to One Class of Vector Optimization Problems in Banach Space

Author(s):

Peter I. Kogut, Rosanna Manzo, and Igor V. Nechay

Department of Differential Equations,
Dnipropetrovsk National University,
Naukova str., 13, 49050 Dnipropetrovsk,
Ukraine
 p.kogut@i.ua

 Dipartimento di Ingegneria Dell’informazione e Matematica Applicata,
Università di Salerno,
Via Ponte Don Melillo, 84084 Fisciano (Sa),
Italy
manzo@diima.unisa.it


 Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan str., 2, 49010
Dnipro
petrovsk,
Ukraine
 i.nechay@i.ua

Abstract:

In this paper, we study vector optimization problems in Banach spaces for essentially nonlinear operator equations with additional control and state constraints. We assume that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. Using the penalization approach we derive both sufficient and necessary conditions for the existence of efficient solutions of the above problems. We also prove the existence of the so-called generalized efficient solutions via the scalarization of some penalized vector optimization problem.



1: Paper Source PDF document

Paper's Title:

A Dynamic Contact Problem for an Electro Viscoelastic Body

Author(s):

Denche M. and Ait Kaki L.

Laboratoire Equations Differentielles,
Departement de Mathematiques,
Universite Constantine 1,
Algeria.

Ecole Normale Superieure,
Departement des Sciences Exactes et Informatique,
Plateau Mansourah, Constantine.
Algeria.

E-mail: m.denche@umc.edu.dz
leilaitkaki@yahoo.fr

Abstract:

We consider a dynamic problem which describes a contact between a piezoelectric body and a conductive foundation. The frictionless contact is modelled with the normal compliance, the electric conditions are supposed almost perfect. We prove the existence of a unique weak solution for almost perfect electric contact.


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