Iterative algorithm for completely generalized set-valued strongly nonlinear mixed variational-like inequalities

A class of completely generalized set-valued strongly nonlinear mixed variational-like inequalities is introduced. The auxiliary principle technique is extended to study this new class of mixed variational-like inequalities. The existence of a solution of the auxiliary problem for this new class of mixed variational-like inequalities is shown. The iterative algorithm for this new class of mixed variational-like inequalities is given by virtue of this existence result. Moreover, the existence of a solution of this new class of mixed variational-like inequalities and the strong convergence of iterative sequences generated by the algorithm are shown. The convergence criteria are different from some early and recent ones presented in the literature. (c) 2005 Elsevier Ltd. All rights reserved.