Hybrid iterative method for solving split variational inclusion problem and fixed-point problem for a finite family of nonexpansive mappings in real hilbert spaces

Abstract

This paper presents a novel iterative approach designed to approximate a unified solution for both split variational inclusion problem and fixed-point problem of finite family of nonexpansive mappings. Within the context of real Hilbert spaces, we establish and validate a strong convergence theorem to achieve this common solution. The method and results presented in this paper extend and unify some recent known results in this field. Finally, a numerical example is used to demonstrate the convergence analysis of the sequences generated by the iterative method.