Algorithmic and analytical approach to the split common fixed points problem

Li-Jun Zhu,Yonghong Yao,Shin Min Kang,Yeong-Cheng Liou

doi:10.1186/1687-1812-2014-172

Abstract

Abstract The split problem, especially the split common fixed point problem, has been studied by many authors. In this paper, we study the split common fixed point problem for the pseudo-contractive mappings and the quasi-nonexpansive mappings. We suggest and analyze an iterative algorithm for solving this split common fixed point problem. A weak convergence theorem is given. MSC:49J53, 49M37, 65K10, 90C25.

Highlights

This article we devote to the split common fixed point problem and study it for the pseudocontractive and quasi-nonexpansive mappings
The split common fixed point problem is a generalization of the convex feasibility problem which is to find a point x∗ satisfying the following: m x∗ ∈ Ci, i=
There are a large number of references on the CQ method for the split feasibility problem in the literature; see, for instance, [ – ]

Summary

Introduction

This article we devote to the split common fixed point problem and study it for the pseudocontractive and quasi-nonexpansive mappings. The split common fixed point problem is a generalization of the convex feasibility problem which is to find a point x∗ satisfying the following:. Where C and Q are two closed convex subsets of two Hilbert spaces H and H , respectively, and A : H → H is a bounded linear operator. There are a large number of references on the CQ method for the split feasibility problem in the literature; see, for instance, [ – ] It is our main purpose in this paper to develop algorithms for the split common fixed point for the pseudo-contractive and quasi-nonexpansive mappings. ([ ]) Let H be a Hilbert space and let {un} be a sequence in H such that there exists a nonempty set ⊂ H satisfying the following:. We may assume that the Lipschitz constant L >

Since ξn

Observe that