Approximation of Fixed Points for E-Type Enriched Nonexpansive Mappings with Applications

Abstract

In this research, we propose an inertial-type iterative scheme constructed by an E-type enriched nonexpansive mappings in the framework of uniformly convex Banach spaces. Strong and weak convergence results along with stability result for the proposed algorithm are presented. Numerical examples and comparisons with well known existing iterative schemes with the help of graphs are presented to demonstrate the efficiency of our proposed scheme. It is shown that the algorithm presented herein converges more faster to fixed point and competitive on the examples considered for this class of mappings. As applications, we apply the scheme to solve variational inequality problems, constrained optimization problems, and split feasibility problems. Moreover, we use the proposed approach to solve a functional differential equation.