Strong convergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions

Atid Kangtunyakarn

doi:10.1186/1687-1812-2011-23

Abstract

In this article, we introduce a new mapping generated by an infinite family of κ i - strict pseudo-contractions and a sequence of positive real numbers. By using this mapping, we consider an iterative method for finding a common element of the set of a generalized equilibrium problem of the set of solution to a system of variational inequalities, and of the set of fixed points of an infinite family of strict pseudo-contractions. Strong convergence theorem of the purposed iteration is established in the framework of Hilbert spaces.

Highlights

Let C be a closed convex subset of a real Hilbert space H, and let G : C × C ® R be a bifunction
We know that the equilibrium problem for a bifunction G is to find x Î C such that
In this article, motivated by Qin et al [11], by using S-mapping, we introduce a new iteration method for finding a common element of the set of a generalized equilibrium problem of the set of solution to a system of variational inequalities, and of the set of fixed points of an infinite family of strict pseudo-contractions

Summary

Introduction

Let C be a closed convex subset of a real Hilbert space H, and let G : C × C ® R be a bifunction. In this article, motivated by Qin et al [11], by using S-mapping, we introduce a new iteration method for finding a common element of the set of a generalized equilibrium problem of the set of solution to a system of variational inequalities, and of the set of fixed points of an infinite family of strict pseudo-contractions. Let E be a uniformly convex Banach space, C be a nonempty closed convex subset of E and S : C ® C be a nonexpansive mapping. Let C be a nonempty closed convex subset of a real Hilbert space H and S : C ® C be a self-mapping of C. Let C be a nonempty closed convex subset of a real Hilbert space.

Main results

Applications