Existence of fixed points of some classes of nonlinear mappings in spaces with weak uniform normal structure

2015 ◽  
Vol 9 ◽  
pp. 4255-4260
Author(s):  
Godwin Amechi Okeke ◽  
Mufutau Adesina Olabiyi
Keyword(s):  
Fixed Points ◽  
Normal Structure ◽  
Uniform Normal Structure ◽  
Nonlinear Mappings

scholarly journals Weak uniform normal structure and iterative fixed points of nonexpansive mappings

1995 ◽  
Vol 68 (1) ◽  
pp. 17-23 ◽  
Author(s):  
T. Domínguez Benavides ◽  
G. López Acedo ◽  
Hong Xu
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Uniform Normal Structure

scholarly journals Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part I

1998 ◽  
Vol 3 (1-2) ◽  
pp. 133-151 ◽  
Author(s):  
Monika Budzyńska ◽  
Tadeusz Kuczumow ◽  
Simeon Reich
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Normal Structure ◽  
Opial Property ◽  
Uniform Normal Structure ◽  
Asymptotic Normal ◽  
Asymptotically Regular

In this paper we introduce the uniform asymptotic normal structure and the uniform semi-Opial properties of Banach spaces. This part is devoted to a study of the spaces with these properties. We also compare them with those spaces which have uniform normal structure and with spaces withWCS(X)>1.

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.

scholarly journals Nearly Contraction Mapping Principle for Fixed Points of Hemicontinuous Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Xavier Udo-utun ◽  
M. Y. Balla ◽  
Z. U. Siddiqui
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Nonlinear Mappings

We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces. We have applied certain results due to Sahu (2005) to obtain conditions for existence—and to introduce an asymptotic iterative process for construction—of fixed points of these hemicontractions with respect to a new auxiliary operator.

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