Auxiliary principle and iterative algorithm for a new system of generalized mixed equilibrium problems in Banach spaces

2011 ◽  
Vol 218 (7) ◽  
pp. 3507-3514 ◽  
Author(s):  
Xie Ping Ding
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Auxiliary Principle ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium ◽  
New System

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.

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