scholarly journals A fixed point theorem for uniformly Lipschitzian mappings in modular vector spaces

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5435-5444 ◽  
Author(s):  
M Alfuraidan ◽  
M.A. Khamsi ◽  
N. Manav
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Variable Exponent ◽  
Normal Structure ◽  
Vector Spaces ◽  
Structure Property ◽  
Uniform Normal Structure ◽  
Lipschitzian Mappings

We give a fixed point theorem for uniformly Lipschitzian mappings defined in modular vector spaces which have the uniform normal structure property in the modular sense. We also discuss this result in the variable exponent space lp(.) = {(xn) ? RN; ?? n=0 ??xn?p(n) < ? for some ? > 0.

scholarly journals Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓp(·)

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 375
Author(s):  
Monther R. Alfuraidan ◽  
Mohamed A. Khamsi
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Successful Treatment ◽  
Variable Exponent ◽  
Triangle Inequality ◽  
Sequence Spaces ◽  
Ekeland Variational Principle ◽  
The Core

In this work, we investigate the modular version of the Ekeland variational principle (EVP) in the context of variable exponent sequence spaces ℓ p ( · ) . The core obstacle in the development of a modular version of the EVP is the failure of the triangle inequality for the module. It is the lack of this inequality, which is indispensable in the establishment of the classical EVP, that has hitherto prevented a successful treatment of the modular case. As an application, we establish a modular version of Caristi’s fixed point theorem in ℓ p ( · ) .

Fixed point theorem for non-expansive mappings on banach spaces with uniformly normal structure

1979 ◽  
Vol 9 (2) ◽  
pp. 121-124 ◽  
Author(s):  
A. A. Gillespie ◽  
B. B. Williams ◽  
V. Lakshmikantham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Normal Structure

scholarly journals The Opial condition in variable exponent sequence spaces with applications

2019 ◽  
Vol 35 (3) ◽  
pp. 273-279
Author(s):  
MOSTAFA BACHAR ◽  
◽  
MOHAMED A. KHAMSI ◽  
MESSAOUD BOUNKHEL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Sequence Space ◽  
Variable Exponent ◽  
Sequence Spaces ◽  
Opial Condition ◽  
Opial Property

In this work, we show an analogue to the Opial property for the coordinate-wise convergence in the variable exponent sequence space. This property allows us to prove a fixed point theorem for the mappings which are nonexpansive in the modular sense.

scholarly journals A common fixed point theorem in strictly convex Menger PM-spaces

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 735-743 ◽  
Author(s):  
Sinisa Jesic ◽  
Rale Nikolic ◽  
Natasa Babacev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Normal Structure ◽  
Strictly Convex ◽  
Common Fixed Point Theorem

In this paper we will define a notions of strictly convex and normal structure in Menger PM-space. Also, existence of a common fixed point for two self-mappings defined on strictly convex Menger PM-spaces will be proved. As a consequence of main result we will give probabilistic variant of Browder's result [3]. Projekat Ministarstva nauke Republike Srbije, br. 174032]

A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings

1991 ◽  
Vol 34 (4) ◽  
pp. 559-562
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence Theorem ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Nonexpansive Semigroups ◽  
Lipschitzian Mappings ◽  
Lipschitzian Semigroup

AbstractAs a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.

scholarly journals Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals Borsuk’s antipodal fixed points theorems for compact or condensing set-valued maps

2018 ◽  
Vol 7 (3) ◽  
pp. 307-311 ◽  
Author(s):  
Najla Altwaijry ◽  
Souhail Chebbi ◽  
Hakim Hammami ◽  
Pascal Gourdel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Large Class ◽  
Point Theorem ◽  
Vector Spaces ◽  
Compact Set ◽  
Topological Vector Spaces ◽  
Locally Convex

AbstractWe give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

Fixed point theorem in subsets of topological vector spaces

2005 ◽  
Vol 340 (11) ◽  
pp. 815-818
Author(s):  
Youcef Askoura ◽  
Christiane Godet-Thobie
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Vector Spaces ◽  
Topological Vector Spaces
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