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 quasi variational inequality in real Banach spaces is designed. We manifest the existence result and verified by an illustrative example. Also, we estimate the approximate solution of a set-valued quasi variational inequality by analyzing the convergence of the proposed inertial iterative algorithm. Further, an extended Weiner-Hopf equation is considered and substantiated that it is analogous to the extended set-valued quasi variational inequality. Finally, we investigate the extended Weiner-Hopf equation by analyzing the convergence of the composed iterative scheme.

Keywords

• Set-valued quasi variational inequality; inertial iterative algorithm; strong convergence; Weiner-Hopf equation