General alternative regularization methods for split equality common fixed-point problem

Abstract

The purpose of this paper is to propose a general alternative regularization algorithm for split equality common fixed-point problem of nonexpansive operator in the framework of infinite-dimensional Hilbert spaces. We prove the strong convergence of the proposed algorithm with the stepsizes chosen by two ways. As a consequence, we obtain strong convergence theorems for split equality common fixed-point problem of firmly-nonexpansive operator and split equality problem. The efficiency of the proposed algorithms is illustrated by some numerical tests.

Keywords:

• Split equality common fixed-point problem
• nonexpansive operators
• strong convergence
• iterative algorithm
• Hilbert space

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61503385]; Open Fund of Tianjin Key Lab for Advanced Signal Processing [grant number 2017ASP-TJ03].