Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces

2011 ◽  
Vol 32 (2) ◽  
pp. 231-240 ◽  
Author(s):  
Xie-ping Ding
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Auxiliary Principle ◽  
Reflexive Banach Spaces ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

scholarly journals On a System of Generalized Mixed Equilibrium Problems Involving Variational-Like Inequalities in Banach Spaces: Existence and Algorithmic Aspects

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
H. Mahdioui ◽  
O. Chadli
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Auxiliary Problem ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Algorithmic Aspect ◽  
Mixed Equilibrium

We study the existence and the algorithmic aspect of a System of Generalized Mixed Equilibrium Problems involving variational-like inequalities (SGMEPs) in the setting of Banach spaces. The approach adopted is based on the auxiliary principle technique and arguments from generalized convexity. A new existence theorem for the auxiliary problem is established; this leads us to generate an algorithm which converges strongly to a solution of (SGMEP) under weaker assumptions. When the study is reduced to the setting of reflexive Banach spaces, then it can be more relaxed by dropping the coercivity condition. The results obtained in this paper are new and improve some recent studies in this field.

scholarly journals An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed andϕ-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Generalized Mixed Equilibrium Problems ◽  
Shrinking Projection Method ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed andϕ-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others.

Sign in / Sign up

Export Citation Format

Share Document