Variational inequality problem with application to convex minimization problem

Abstract

In this study, we propose a new iterative algorithm and prove convergence results in Banach space. We also present a modified algorithm for identifying the common elements of the set of variational inequalities and fixed point of nonexpansive mappings in a Hilbert space. Under some mild circumstances, we investigate the convergence criterion of given algorithm. Furthermore, we solve the convex minimization problem using the modified iterative algorithm. The theoretical results obtained here are validated using numerical examples. Our findings can be viewed as an enhancement, improvement, and supplement to the already established results.