Existence and algorithm of solutions for nonlinear mixed variational-like inequalities in Banach spaces

In this paper, we study a new class of nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to author, we first prove an existence uniqueness theorem of solutions for the nonlinear mixed variational-like inequalities. Next, we extend the auxiliary problem technique under reflexive Banach space setting to suggest and analyze an innovative iterative algorithm to compute the approximate solutions of the nonlinear mixed variational-like inequalities. The convergence criteria of the iterative algorithm is also given. These results improve and generalize many known results in recent literature.