General algorithm for nonlinear variational-like inequalities in reflexive Banach spaces (Q1390143)

The author studies a class of general nonlinear variational-like inequalities in reflexive Banach spaces. In particular, by using a minimax inequality that he had obtained earlier, he is able to prove in this paper very interesting existence and uniqueness theorems for solutions of the general nonlinear variational-like inequalities. He extends the auxiliary principle technique in a reflexive Banach space setting in order to compute the approximate solutions of the general nonlinear variational-like inequalities. The paper concludes with some very well presented convergence criteria.