EXISTENCE AND CONVERGENCE RESULTS FOR THE SYSTEM OF GENERALIZED MIXED VARIATIONAL-LIKE INEQUALITIES WITH MULTI-VALUED MAPPINGS

The goal of this article is to study generalized mixed variational-like inequalities with multi-valued mappings over the product of sets and the system of generalized mixed variational-like inequalities with multi-valued mappings in topological vector spaces, moreover both the problems are equivalent. By employing auxiliary principle method, we develop an iterative algorithm to determine the approximate solutions of our problems. Under some suitable conditions and well-known theorems, we prove existence and uniqueness of solutions for our problems. Finally, we analyze the strong convergence of approximate solutions to the unique solution of the system of generalized mixed variational-like inequalities with multi-valued mappings. These results are more general than some known result in this field.