scholarly journals Viscosity Approximation Methods for Generalized Mixed Equilibrium Problems and Fixed Points of a Sequence of Nonexpansive Mappings

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Wei-You Zeng ◽  
Nan-Jing Huang ◽  
Chang-Wen Zhao
Keyword(s):  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Viscosity Approximation Methods ◽  
Mixed Equilibrium

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 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 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 Strong Convergence Theorems for Family of Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Yekini Shehu
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium problems, and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element of the three sets. We give some applications of our results. Our results extend important recent results.

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