scholarly journals Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces

2008 ◽  
Vol 2008 (1) ◽  
pp. 583082 ◽  
Author(s):  
Somyot Plubtieng ◽  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Convex Feasibility Problems ◽  
Relatively Nonexpansive Mappings ◽  
Convex Feasibility ◽  
Relatively Nonexpansive ◽  
Hybrid Iterative Methods

scholarly journals On cyclic relatively nonexpansive mappings in generalized semimetric spaces

2015 ◽  
Vol 16 (2) ◽  
pp. 99 ◽  
Author(s):  
Moosa Gabeleh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Relatively Nonexpansive ◽  
The Stability ◽  
Semimetric Spaces

In this article, we prove a fixed point theorem for cyclic relatively nonexpansive mappings in the setting of generalized semimetric spaces by using a geometric notion of seminormal structure and then we conclude some results in uniformly convex Banach spaces. We also discuss on the stability of seminormal structure in generalized semimetric spaces.

scholarly journals A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mei Yuan ◽  
Xi Li ◽  
Xue-song Li ◽  
John J. Liu
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Projection Method ◽  
Convergence Theorem ◽  
Projection Operator ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalizedf-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.

scholarly journals Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xianbing Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Bounded Sets

It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.

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