scholarly journals Iterative approximation methods for mixed equilibrium problems for a countable family of quasi-ϕ-asymptotically nonexpansive multivalued mappings in Banach spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Rabian Wangkeeree ◽  
Pakkapon Preechasilp
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Countable Family ◽  
Multivalued Mappings ◽  
Approximation Methods ◽  
Iterative Approximation ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
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 Bilevel mixed equilibrium problems in Banach spaces : existence and algorithmic aspects

2011 ◽  
Vol 1 (3) ◽  
pp. 549-561 ◽  
Author(s):  
Ouayl Chadli ◽  
◽  
Hicham Mahdioui ◽  
Jen-Chih Yao ◽  
◽  
...  
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium
Sign in / Sign up

Export Citation Format

Share Document