Auxiliary principle and iterative algorithm for a system of generalized strongly nonlinear mixed variation-like inequalities in banach spaces

Abstract

In this paper we introduce a system of generalized strongly nonlinear mixed variational-like inequalities in Banach spaces. An existence theorem for auxiliary problem is established. By exploiting this theorem, we suggest an algorithm for solving the system of generalized strongly nonlinear mixed variational-like inequalities, prove the existence of a unique solution of the system of generalized strongly nonlinear mixed variationallike inequalities and discuss the convergence of the algorithm.