A Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Finding Fixed Points of a Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces

2021 ◽  
Author(s):  
Vahid Darvish ◽  
Kittisak Jantakarn ◽  
Anchalee Kaewcharoen ◽  
Nader Biranvand
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Generalized Mixed Equilibrium Problems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium

scholarly journals Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Zhaoli Ma ◽  
Lin Wang ◽  
Yunhe Zhao
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium

We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.

scholarly journals A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Yekini Shehu
Keyword(s):  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Generalized Mixed Equilibrium Problems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalizedf-projection operator. Using this result, we discuss strong convergence theorem concerning generalH-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.

scholarly journals The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Kriengsak Wattanawitoon ◽  
Poom Kumam
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Mixed Equilibrium Problems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium ◽  
Modified Block

The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many known recent results in the literature.

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 A New Hybrid Algorithm for Solving a System of Generalized Mixed Equilibrium Problems, Solving a Family of Quasi--Asymptotically Nonexpansive Mappings, and Obtaining Common Fixed Points in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
J. F. Tan ◽  
S. S. Chang
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The main purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi--asymptotically nonexpansive mappings, and null spaces of finite family of -inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. The results presented in the paper improve and extend the corresponding results announced by some authors.

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