The methods for variational inequality problems and fixed point of κ-strictly pseudononspreading mapping

Atid Kangtunyakarn

doi:10.1186/1687-1812-2013-171

Abstract

In this paper, we introduce the methods for finding a common element of the set of fixed points of a κ-strictly pseudononspreading mapping and a finite family of the set of solutions of variational inequality problems. The strong convergence theorem of the proposed method is established under some suitable control conditions. Moreover, by using our main result, we prove interesting theorem involving an iterative scheme for finding a common element of the set of fixed points of a κ-strictly pseudononspreading mapping and a finite family of the set of fixed points of a -strictly pseudocontractive mappings.

Highlights

Let C be a nonempty closed convex subset of a real Hilbert space H
Recall that the mapping T : C → C is said to be nonexpansive if Tx – Ty ≤ x – y for all x, y ∈ C
In, Takahashi and Toyoda [ ] proved a convergence theorem for finding a common element of the set of fixed points of nonexpansive mappings and the set of solutions of variational inequalities for α-inverse strongly monotone mappings as follows

Summary

Introduction

1 Introduction Let C be a nonempty closed convex subset of a real Hilbert space H. In , Takahashi and Toyoda [ ] proved a convergence theorem for finding a common element of the set of fixed points of nonexpansive mappings and the set of solutions of variational inequalities for α-inverse strongly monotone mappings as follows. Let K be a closed convex subset of a real Hilbert space H.

Results

Conclusion