Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities

Abstract

We introduce and study a system of generalized nonlinear mixed variational-like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. First, the existence of solutions of the auxiliary problems for the SGNMVLIP is shown. Second, an iterative algorithm for solving the SGNMVLIP is constructed by using this existence result. Finally, not only the existence of solutions of the SGNMVLIP is shown but also the convergence of iterative sequences generated by the algorithm is also proven. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in the literature.