Nonexpansive mappings and proximinality in normed almost linear spaces

1992 ◽  
pp. 80-87
Author(s):  
Geetha S. Rao ◽  
T. L. Bhaskaramurthi
Keyword(s):  
Nonexpansive Mappings ◽  
Linear Spaces

scholarly journals Contractibility of Fixed Point Sets of Mean-Type Mappings

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
S. Iampiboonvatana ◽  
P. Chaoha
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Point Sets ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Convex Setting ◽  
Fixed Point Sets

We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.

scholarly journals Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Mujahid Abbas ◽  
Basit Ali ◽  
Salvador Romaguera
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Contractive Mapping ◽  
Linear Spaces ◽  
Complete Metric Spaces ◽  
Normed Linear Spaces ◽  
Fixed Point Result ◽  
Invariant Approximation ◽  
New Type

Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalizedF-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces

Sub-normed Z-linear Spaces on Commutative Semi-group

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  
Semi Group ◽  
Linear Spaces

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

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