Auxiliary Principle and Iterative Algorithms for Generalized Set-Valued Strongly Nonlinear Mixed Variational-like Inequalities

In this paper, we extend the auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities. We prove the existence of a solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities, construct the iterative algorithm for the generalized set-valued strongly nonlinear mixed variational- like inequalities, and show the existence of a solution of the generalized set-valued strongly nonlinear mixed variational-like inequality by using the auxiliary principle technique. We also prove the convergence of iterative sequences generated by the algorithm