Hybrid Algorithm for Finding Common Elements of the Set of Generalized Equilibrium Problems and the Set of Fixed Point Problems of Strictly Pseudocontractive Mapping

Atid Kangtunyakarn

doi:10.1155/2011/274820

Abstract

The purpose of this paper is to prove the strong convergence theorem for finding a common element of the set of fixed point problems of strictly pseudocontractive mapping in Hilbert spaces and two sets of generalized equilibrium problems by using the hybrid method.

Highlights

Let C be a closed convex subset of a real Hilbert space H, and let F : C × C → R be a bifunction
Ishikawa proved the following strong convergence theorem of pseudocontractive mapping
In order to prove a strong convergence theorem of Mann algorithm 1.12 associated with strictly pseudocontractive mapping, in 2006, Marino and Xu 7 proved the following theorem for strict pseudocontractive mapping in Hilbert space by using CQ method

Summary

Introduction

Let C be a closed convex subset of a real Hilbert space H, and let F : C × C → R be a bifunction. Ishikawa proved the following strong convergence theorem of pseudocontractive mapping. In order to prove a strong convergence theorem of Mann algorithm 1.12 associated with strictly pseudocontractive mapping, in 2006, Marino and Xu 7 proved the following theorem for strict pseudocontractive mapping in Hilbert space by using CQ method. Let T : C → C be a κ-strict pseudocontraction for some 0 ≤ κ < 1, and assume that the fixed point set F T of T is nonempty. The motivation of 1.14 , 1.15 , and the research in this direction, we prove the strong convergence theorem for finding solution of the set of fixed points of strictly pseudocontractive mapping and two sets of generalized equilibrium problems by using the hybrid method

Preliminaries

Main Result

Applications