Iterative Scheme of Strongly Nonlinear General Nonconvex Variational Inequalities Problem

Chanan Sudsukh, Issara Inchan

Abstract

A mapping T1 satisfying the Lipschitz continuous and strongly monotone and T2 satisfying Lipschitz continuousbut we get that T1+T2 is Lipschitz continuous but not necessary the strongly monotone mapping. Inthis work, we suggest and analyze an iterative scheme for solving the strongly nonlinear general nonconvexvariational inequalities by using projection technique and Wiener-Hopf technique. We prove strong convergenceof iterative scheme to the solution of the strongly nonlinear general nonconvex variational inequalitiesrequires to the modified mapping T which is Lipschitz continuous but not strongly monotone mapping. Ourresult can be viewed and improvement the result of E. Al-Shemas [14].