An Iterative Approach with the Inertial Method for Solving Variational-like Inequality Problems with Multivalued Mappings in a Banach Space

Abstract

We formulate an iterative approach employing the inertial technique to approximate the anticipated solution for a generalized mixed variational-like inequality, as well as variational inequality and fixed point problems associated with a relatively nonexpansive multivalued mapping within the context of a real Banach space. Additionally, we delve into the robust convergence of our suggested algorithm. Furthermore, we highlight certain implications and present numerical observations to underscore the significance of our findings. The proposed theorem extends and consolidates several previously published works.