Cyclic uniform Lipschitzian mappings and proximal uniform normal structure

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Abhik Digar ◽  
G. Sankara Raju Kosuru
Keyword(s):  
Normal Structure ◽  
Uniform Normal Structure ◽  
Lipschitzian Mappings

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 Common fixed point theorems for commutingk-uniformly Lipschitzian mappings

2001 ◽  
Vol 25 (3) ◽  
pp. 145-152
Author(s):  
M. Elamrani ◽  
A. B. Mbarki ◽  
B. Mehdaoui
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Uniform Normal Structure ◽  
Lipschitzian Mappings ◽  
Common Fixed Point Theorems

We give a common fixed point existence theorem for any sequence of commutingk-uniformly Lipschitzian mappings (eventually, fork=1for any sequence of commuting nonexpansive mappings) defined on a bounded and complete metric space(X,d)with uniform normal structure. After that we deduce, by using the Kulesza and Lim (1996), that this result can be generalized to any family of commutingk-uniformly Lipschitzian mappings.

scholarly journals On the modulus ofU-convexity

2005 ◽  
Vol 2005 (1) ◽  
pp. 59-66 ◽  
Author(s):  
Satit Saejung
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Normal Structure ◽  
Uniform Normal Structure

We prove that the moduli ofU-convexity, introduced by Gao (1995), of the ultrapowerX˜of a Banach spaceXand ofXitself coincide wheneverXis super-reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove thatuX(1)>0implies that bothXand the dual spaceX∗ofXhave uniform normal structure and hence the “worth” property in Corollary 7 of Mazcuñán-Navarro (2003) can be discarded.

Fixed point theorems for uniformly generalized Kannan type semigroup of self-mappings

2017 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
AHMED H. SOLIMAN ◽  
MOHAMMAD IMDAD ◽  
MD AHMADULLAH
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Real Banach Space ◽  
Normal Structure ◽  
Uniform Normal Structure

In this paper, we consider a new uniformly generalized Kannan type semigroup of self-mappings defined on a closed convex subset of a real Banach space equipped with uniform normal structure and employ the same to show that such semigroup of self-mappings admits a common fixed point provided the underlying semigroup of self-mappings has a bounded orbit.

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