International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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Operational formulae of the generalized
hypergeometric matrix functions and related
matrix polynomials

M. Abdalla , H. Abd-Elmageedb , M. Abul-Ez

Dept. of Math., Faculty of Science, South Valley University, Qena 83523, Egypt.

Dept. of Math., Faculty of Science, South Valley University, Qena 83523, Egypt.

Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

ABSTRACT

The aim of this article is to present an overview of the modern de-
velopments around the theme of multivariable hypergeometric matrix
functions (MHMFs). Operator representations of multivariable hy-
pergeometric functions and certain classes of orthogonal matrix poly-
nomials are established here by a new technique.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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On the matrix versions of Srivastava's triple hypergeometric functions

M. Abdalla

Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

ABSTRACT

This paper deals with the study of the Srivastava's triple hypergeometric matrix functions. The
convergent properties, an integral representation of these functions
and contiguous function relations are
obtained. Some results coming from operating the differential
operator on Srivastava's triple hypergeometric matrix functions are
established. Moreover a solution of certain partial differential
equation are given.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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12

Some results on Appell hypergeometric matrix functions

H. ABD-ELMAGEED , M. ABUL-EZ , Z. KISHKA , A. ABDEL RADY

Department of Mathematics Faculty of Science South Valley University Qena 83523 Egypt

Department of Mathematics Faculty of Science Sohag University Sohag 82524 Egypt

Department of Mathematics Faculty of Science Sohag University Sohag 82524 Egypt

Department of Mathematics Faculty of Science South Valley University Qena 83523 Egypt

ABSTRACT

In this paper we have established result for the Appell's hypergeometric matrix functions. An integral representation of these functions, generating functions and reduction formulas are derived here. Furthermore, certain relations are obtained by acting a diﬀerential operator to Appell matrix functions arguments have also been discussed.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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12

FIXED POINT AND CONVERGENCE THEOREM FOR
GENERALIZED ϕ WEAK CONTRACTIONS AND
{a; b; c; r} GENERALIZED CYCLIC CONTRACTIONS IN
QUASI METRIC SPACES

Sahar Mohamed Ali Abou Bakr

Ain Shams University, Faculty of Science, Department of Mathematics, Cairo, Egypt.

ABSTRACT

We prove the existence of only one common fixed point of two mappings, in particular; proves the existence of unique fixed point of some generalized contraction, introduces new type of {a, b, c; r} generalized cyclic contraction, proves the existence of unique fixed point of such mappings; all are defined on complete quasi metric spaces, and then establishes a convergence theorem for a sequence of fixed points of a sequence of generalized cyclic contractions to the unique fixed point of a given generalized cyclic contraction S. This research extends and generalizes results previously proved.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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12

MORE GENERAL COMMON FIXED POINT THEOREMS UNDER A NEW CONCEPT

Hakima BOUHADJERA

Laboratory of Applied Mathematics Badji Mokhtar-Annaba University P.O. Box 12, 23000 Annaba, Algeria

ABSTRACT

A general common fixed point theorem for two pairs of weakly subsequentially continuous mappings (recently introduced) satisfying a significant estimated implicit function is proved. An extension of this results thereby obtained. Our results assert the existence and uniqueness of
common fixed points in several cases.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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12

Some Properties of Certain Subclasses of Analytic Functions Defined by using An Integral Operator

A. H. Hassan , D. A. Mohan

Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Faculty of Science, Zagazig University, Zagazig 44519, Egypt

ABSTRACT

In this paper, by using the subordination principle we introduce and study new subclasses of analytic
functions with negative coefficients defined on the open unit disk. We obtain numerous sharp results including (for example) coefficient estimates, distortion theorem, radii of starlikeness and convexity. Moreover, we deduce some results according to the modified Hadamard product of functions belonging to these subclasses.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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Quaternion-Valued Functions and Lacunary Series Expansions in Hyperholomorphic $F^{\alpha}_{G}(p,q,s)$ Spaces

Mohamed Abdelrahman Ahmed , Alaa Kamal Mohamed , Taha Ibrahim Yassen Moursy

Professor of Mathematics, Faculty of Science - Assiut University- Egypt

Port Said University, Faculty of Science, Department of Mathematics,Port Said, Egypt

Port Said University, Faculty of Science, Department of Mathematics,Port Said, Egypt

ABSTRACT

The purpose of this paper is to define a new class of hyperholomorphic functions, the so called $F^{\alpha}_{G}(p,q,s)$ Spaces. For this class we obtain characterizations by ${\mathcal{B}}^{\alpha}$ spaces. Moreover, we characterize the hyperholomorphic $F^{\alpha}_{G}(p,q,s)$ functions by the coefficients of certain lacunary series expansions in Clifford analysis.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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Fixed Point Theorems in Weak Quasi Partial Metric Spaces and it's Application

A. M. Zidan , M. A. Barakat

Department of Mathematics, Faculty of Science, Al-Azhar University, Assuit branch, Egypt.

Department of Mathematics, Faculty of Science, Al-Azhar University, Assuit branch, Egypt.

ABSTRACT

We present a New generalized fixed point theorems in weak quasi partial metric spaces for cyclic compatabl contraction . Our result extend some known results duo to Barakat et.al. [1]. Also, in order to illustrate our results, we present the study about the existence and uniqueness of solutions of the functional equation.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

9

12

A NEW GENERALIZED S-ALGORITHM VIA ADMISSIBLE APPROACH TO COMMON FIXED POINTS OF GENERAL-TYPE CONTRACTION MAPPINGS

Ali Mohamed Saddeek , Sayed Attia Ahmed

Department of Mathematics, Faculty of Science, Assiut University, Assiut , Egypt

Department of Mathematics, Faculty of Science, Assiut University, Assiut , Egypt,,,Umm Al Qura University, Jamoum University College, Makka, Saudi Arabia

ABSTRACT

In this paper, a new generalized S-algorithm in terms of admissible and generalized admissible mappings for approximating common fixed points of three mappings satisfying general contraction type conditions is introduced and its strong convergence is proved in uniformly convex Banach spaces. The results improve and generalize the main results of several authors.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

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A Novel Subclasses of Bi-Univalent Analytic Functions Defined by Using Q-Calculus

A. H. Hassan

Department of Mathematics, Faculty of Science, Zagazig University

ABSTRACT

In this paper, by using the q-derivative we introduce certain generalized subclasses of normalized (f(0)=f'(0)-1=0) bi-univalent analytic functions. For functions belonging to the subclass under investigation, we ﬁnd estimates on the Maclaurin coeffcients |a_2| and |a_3|. Some earlier results are improved and some special cases are pointed out.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

11

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Further Properties of Certain Class of Analytic Functions Associated with Bessel-Type Operator

A. H. Hassan

Faculty of Science, Zagazig University

ABSTRACT

In this paper we investigate some subordination properties of certain linear operator associated with the well-known Bessel functions. Also, we investigated some estimates and sufficient starlike conditions of certain subclass of univalent functions defined in the unit disc.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Functional Analysis

12

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Second Order Optimality Conditions For Semilinear Elliptic Optimal Control Problem Infinite Order With Pointwise Mixed Control –State Constraints

Somiah Elzahaby , S. Al-Tamemy

Al-Azhar University[Girls Branch], Faculty of Science, Mathematics Dept.

Al-Azhar University[Girls Branch], Faculty of Science, Mathematics Dept.

ABSTRACT

In this paper a semiliner elliptic optimal control problem of infinite order with mixed control – state constraints are studied. The existence of regular Lagrange multipliers, first – order necessary and Second order sufficient conditions are obtained.