A New Parallel Inertial Splitting Algorithm for Inclusion and Fixed Point Problems in Banach Spaces

Abstract

This article proposes a new parallel method with an inertial extrapolation term for solving monotone inclusion and fixed-point problems involving a finite family of maximal monotone operators and Bregman strongly nonexpansive mappings in the setting of a reflexive Banach space. We establish a strong convergence result for the proposed iterative method without requiring knowledge of the Lipschitz constant of the underlying functions. Additionally, we provide a numerical comparison of our method's performance with existing methods in the literature. Numerical illustrations suggest that the proposed method is competitive and promising. Furthermore, we demonstrate an application of the algorithm in restoring test images degraded by motion blur and random noise. The results indicate that our method achieves superior restoration quality compared to existing methods.