scholarly journals A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Problems ◽  
Reflexive Banach Spaces ◽  
Extragradient Algorithm

scholarly journals A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1487-1497
Author(s):  
Sun Cho
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Reflexive Banach Space ◽  
Fixed Point Problems ◽  
Projection Algorithm ◽  
Reflexive Banach Spaces

In this paper, a monotone Bregan projection algorithm is investigated for solving equilibrium problems and common fixed point problems of a family of closed multi-valued Bregman quasi-strict pseudocontractions. Strong convergence is guaranteed in the framework of reflexive Banach spaces.

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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