An iterative algorithm to approximate a common element of the set of common fixed points for a finite family of strict pseudo-contractions and of the set of solutions for a modified system of variational inequalities

Atid Kangtunyakarn

doi:10.1186/1687-1812-2013-143

Abstract

In this paper, we introduce a new iterative algorithm for finding a common element of the set of fixed points of a finite family of -strictly pseudo-contractive mappings and the set of solutions of new variational inequalities problems in Hilbert space. By using our main results, we obtain an interesting theorem involving a finite family of κ-strictly pseudo-contractive mappings and two sets of solutions of the variational inequalities problem.

Highlights

Let H be a real Hilbert space whose inner product and norm are denoted by · and ·, ·, respectively
It is easy to see that every noexpansive mapping is a κ-strictly pseudo-contractive mapping
From the motivation of [ ] and the research in the same direction, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of κi-strictly pseudo-contractive mappings and the set of solutions of a modified general system of variational inequalities problems

Summary

Introduction

Let H be a real Hilbert space whose inner product and norm are denoted by · and ·, · , respectively. In , Ceng et al [ ] introduce and studied a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space as follows.

Results

Conclusion