Paper's Title:

On ε-simultaneous Approximation in Quotient Spaces

Author(s):

H. Alizadeh, Sh. Rezapour, S. M. Vaezpour

Department of Mathematics, Aazad
Islamic University, Science and Research Branch, Tehran,
Iran

Department of Mathematics, Azarbaidjan
University of Tarbiat Moallem, Tabriz,
Iran

Department of Mathematics, Amirkabir
University of Technology, Tehran,
Iran

alizadehhossain@yahoo.com
sh.rezapour@azaruniv.edu
vaez@aut.ac.ir

URL:http://www.azaruniv.edu/~rezapour
URL:http://math-cs.aut.ac.ir/vaezpour

Abstract:

The purpose of this paper is to develop a theory of best simultaneous approximation to ε-simultaneous approximation. We shall introduce the concept of ε-simultaneous pseudo Chebyshev, ε-simultaneous quasi Chebyshev and ε-simultaneous weakly Chebyshev subspaces of a Banach space. Then, it will be determined under what conditions these subspaces are transmitted to and from quotient spaces.

Paper's Title:

Approximation of an AQCQ-Functional Equation and its Applications

Author(s):

Choonkil Park and Jung Rye Lee

Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133-791,
Korea;

Department of Mathematics,
Daejin University,
Kyeonggi 487-711,
Korea

baak@hanyang.ac.kr
jrlee@daejin.ac.kr

Abstract:

This paper is a survey on the generalized Hyers-Ulam stability of an AQCQ-functional equation in several spaces. Its content is divided into the following sections:

1. Introduction and preliminaries.

2. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: direct method.

3. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: fixed point method.

4. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: direct method.

5. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: fixed point method.

6. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: direct method.

7. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: fixed point method.

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.

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.

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