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

Hicham Mahdioui | Zendy; Ouayl Chadli | Zendy

Open Access

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

Author(s) -

Hicham Mahdioui,

Ouayl Chadli

Publication year - 2012

Publication title -

advances in operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.379

H-Index - 14

eISSN - 1687-9155

pISSN - 1687-9147

DOI - 10.1155/2012/843486

Subject(s) - banach space , convexity , mathematics , variational inequality , pure mathematics , uniformly convex space , eberlein–šmulian theorem , lp space , economics , financial economics

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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