Inertial Modified S-Iteration Process for Split Monotone Inclusion and Fixed Point Problem In Real Hilbert Space

TL;DR

This paper introduces an inertial modified S-iteration method to efficiently find common solutions to split monotone inclusion and fixed point problems in Hilbert spaces, with proven convergence and numerical validation.

Contribution

It develops a novel inertial S-iteration algorithm that accelerates convergence for solving split monotone inclusion and fixed point problems, with strong convergence guarantees.

Findings

The algorithm converges strongly under mild conditions.

Numerical example demonstrates effective acceleration.

Method applicable to real Hilbert spaces.

Abstract

In this article we present a modified S-iteration process that we combine with inertial extrapolation to find a common solution to the split monotone inclusion problem and the fixed point problem in real Hilbert space.Our goal is to establish a strong convergence theorem for approximating a common solution.Under some mild conditions,the problem can be solved. We also provide a numerical example to show that our algorithms acceleration works well.