The split common null point problem for generalized resolvents and nonexpansive mappings in Banach spaces

TL;DR

This paper introduces a new method for solving the split common null point problem in Banach spaces using generalized resolvents and nonexpansive mappings, providing a strong convergence theorem even with errors.

Contribution

It develops a novel strong convergence theorem for the split common null point problem in Banach spaces employing generalized resolvents and an infinite family of nonexpansive mappings.

Findings

Established a strong convergence theorem for the problem

Utilized generalized resolvents and projections in Banach spaces

Proved convergence in the presence of errors

Abstract

In this paper, the split common null point problem in two Banach spaces is considered. Then, using the generalized resolvents of maximal monotone operators and the generalized projections and an infinite family of nonexpansive mappings, a strong convergence theorem for finding a solution of the split common null point problem in two Banach spaces in the presence of a sequence of errors will be proved.