MODIFIED INERTIAL HYBRID SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS FOR AN INFINITE FAMILY OF MULTIVALUED RELATIVELY NONEXPANSIVE MAPPINGS IN BANACH SPACES WITH APPLICATIONS

Abstract

One of the most interesting and important problems in the theory of variational inequalities is the study of efficientiterative schemes for finding approximate solutions and the convergence analysis of algorithms. In this article, we introduce anew inertial hybrid subgradient extragradient method for approximating a common solution of monotone variational inequalities and fixed pointproblems for an infinite family of relatively nonexpansive multivalued mappings in Banach spaces. In our proposed method, the projection ontothe feasible set is replaced with a projection onto certain half spaces, which makes the algorithm easy to implement. We incorporateinertial term into the algorithm, which helps to improve the rate of convergence of the proposed method. Moreover, we prove a strongconvergence theorem and we apply our results to approximate common solutions of variational inequalities and zero point problems, andto finding a common solution of constrained convex minimization and fixed point problems in Banach spaces. Finally, we present a numericalexample to demonstrate the efficiency and the advantages of the proposed method, and we compare it with some related methods. Our results extendand improve some recent works both in Hilbert spaces and Banach spaces in this direction.