Viscosity iteration algorithms for nonlinear variational inclusions and fixed point problems in Banach spaces

2013 ◽  
Vol 45 (1-2) ◽  
pp. 165-181 ◽  
Author(s):  
Ying Liu ◽  
Yongli Chen
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Problems ◽  
Variational Inclusions

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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