The split feasibility and fixed point equality problems for quasi-nonexpansive mappings in Hilbert spaces

TL;DR

This paper introduces the split feasibility and fixed point equality problems (SFFPEP) in Hilbert spaces, proposes an iterative solution algorithm, and proves its convergence, extending existing split feasibility problem frameworks.

Contribution

It presents a new problem formulation (SFFPEP), an iterative algorithm for its solution, and convergence analysis, generalizing previous split feasibility and fixed point problems.

Findings

Convergence of the proposed algorithm is established.

Numerical examples support the theoretical results.

SFFPEP generalizes several existing problems.

Abstract

In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert spaces. Furthermore, we study the convergence of the proposed algorithm. At the end, we give numerical example that illustrate our theoretical result. The SFFPEP is a generalization of the split feasibility problem (SFP), split feasibility and fixed point problems (SFFPP) and split equality fixed point problem (SEFPP).