Existence and convergence theorems for the new system of generalized mixed variational inequalities in Banach spaces

Abstract

In this article, we introduce and consider the three-step iterative algorithms for solving a new system of generalized mixed variational inequalities involving different three multi-valued operators. In this study, we use a generalized f-projection method for finding the solutions of generalized system of mixed variational inequalities in Banach spaces. Our result in this article improves and generalizes some known corresponding results in the literature.

Strong Convergence of Three Step Iteration Process for Nonexpansive and Strongly Pseudocontractive Mappings Apurva Kumar Das, Shailesh Dhar Diwan and Samir Dashputre

“…In a paper Rashwan [20] studied the convergence of Mann iterates to a common fixed point for a pair of mappings in normed space. Many papers have been published on the iterative approximation of fixed points of Lipschitz strongly pseudocontractive mappings using the Ishikawa iteration process (see, e.g., [3,12,13,19,24,28,31] and the references cited therein).…”