Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces

Aihong Wang

doi:10.1155/2012/150145

Abstract

We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of the solutions of the equilibrium problem and the set of fixed points of infinitely strict pseudocontractive mappings. Strong convergence theorems are established in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently.

Highlights

Let H be a real Hilbert space and let C be a nonempty convex subset of H
We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of the solutions of the equilibrium problem and the set of fixed points of infinitely strict pseudocontractive mappings
Let Φ be a bifunction from C × C to R, where R is the set of real numbers

Summary

Introduction

Let H be a real Hilbert space and let C be a nonempty convex subset of H. He obtained that the sequence xn generated by 1.9 converges to a point q in F T , which is the unique solution of the variational inequality γf − A q, p − q ≤ 0, p ∈ F T .

Results

Conclusion