scholarly journals A relaxed hybrid shrinking iteration approach to solving generalized mixed equilibrium problems for totally quasi-ϕ-asymptotically nonexpansive mappings

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Wei-Qi Deng
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

scholarly journals Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Jinhua Zhu ◽  
Shih-Sen Chang ◽  
Min Liu
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Common Element ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is first to introduce the concept oftotal quasi-ϕ-asymptotically nonexpansive mappingwhich contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

scholarly journals A New Iterative Method for Solving a System of Generalized Mixed Equilibrium Problems for a Countable Family of Generalized Quasi-ϕ-Asymptotically Nonexpansive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wei-Qi Deng
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Strong Convergence Theorem ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

By using a specific way of choosing the indexes, we introduce an up-to-date iterative algorithm for approximating common fixed points of a countable family of generalized quasi-ϕ-asymptotically nonexpansive mappings and obtain a strong convergence theorem under some suitable conditions. As application, an iterative solution to a system of generalized mixed equilibrium problems is studied. The results extend those of other authors, in which the involved mappings consist of just finite families.

scholarly journals A New Hybrid Algorithm for a System of Generalized Mixed Equilibrium Problems and Fixed Point of Quasi--Asymptotically Nonexpansive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Jinhua Zhu ◽  
Shih-Sen Chang
Keyword(s):  
Hybrid Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is to use a new hybrid algorithm for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for an infinite family of quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

scholarly journals Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-27 ◽  
Author(s):  
Siwaporn Saewan ◽  
Poom Kumam
Keyword(s):  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is to present a new hybrid block iterative scheme by the generalizedf- projection method for finding a common element of the fixed point set for a countable family of uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.

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.

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.

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