Auxiliary Principle and Iterative Algorithm for a Generalized Nonlinear Mixed Quasi-variational-like Inequality

Abstract

In this paper, we employ the auxiliary principle technique to study a generalized nonlinear mixed quasi-variational-like inequality in Hilbert spaces. Fist, we establish the existence and uniqueness of solution of the corresponding auxiliary generalized nonlinear mixed quasi-variational-like inequality by making use of minimizing sequence of a convex function. Then based on the existence result, we construct an iterative algorithm for finding approximate solution to the exact solution of the generalized nonlinear mixed quasi-variational-like inequality. Our results extend, improve and unify some known results in the literature.