Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Abstract

In this article, a projection type two step inertial iterative scheme for investigating set-valued quasivariational inequality in real Banach spaces is designed. We manifest the existence result and verified by an illustrativeexample. Also, we estimate the approximate solution of a set-valued quasi variational inequality by analyzing theconvergence of the proposed inertial iterative algorithm. Further, an extended Weiner-Hopf equation is consideredand substantiated that it is analogous to the extended set-valued quasi variational inequality. Finally, we investigatethe extended Weiner-Hopf equation by analyzing the convergence of the composed iterative scheme.