Self-Adaptive Algorithms for the Split Common Fixed Point Problem of the Demimetric Mappings

Xinhong Chen,Jianying He,Liping Gong,Yanlai Song

doi:10.4236/jamp.2019.710150

Abstract

The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces. Moreover, our algorithm does not need any prior information of the operator norm. Weak and strong convergence theorems are given under some mild assumptions. The results in this paper are the extension and improvement of the recent results in the literature.

Highlights

Let H1 and H2 be two real Hilbert spaces
The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set
We present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces

Summary

Introduction

Let H1 and H2 be two real Hilbert spaces. Let S : H1 → H1 and T : H2 → H2 be two nonlinear mappings. We denote the fixed point sets of S and T by F (S ) and F (T ) , respectively. Let A : H1 → H2 be a bounded linear operator with its adjoint A*. We consider the following split common fixed point problem: Finding x ∈ H1 such that x ∈ F (S ) and Ax ∈ F (T ).

Objectives

Results

Conclusion