Iterative Methods for Solving the Monotone Inclusion Problem and the Fixed Point Problem in Banach Spaces

Prasit Cholamjiak, Pongsakorn Sunthrayuth, Akarate Singta, Kanikar Muangchoo

Abstract

In this work, we propose two iterative algorithms for solving the monotone inclusion problem and the fixed point problem of a relatively nonexpansive mapping in the framework of Banach spaces. We prove the strong convergence theorems of the proposed algorithms under some suitable assumptions. Furthermore, some numerical experiments of proposed algorithms to compressed sensing in signal recovery are presented. Our results improve and generalize many recent and important results in the literature.