Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces
In this paper, we study a class of mixed quasi-variational-like inclusion with a bifunction in reflexive Banach spaces. By applying a minimax inequality due to the first author, some existence and uniqueness theorems of solutions for the mixed quasi-variational-like inclusions are proved. Next, by applying the auxiliary variational inequality technique, we suggest an iterative algorithm to compute the approximate solutions of the mixed quasi-variational-like inclusions. The convergence criteria of the algorithm is studied under quite mild conditions. Our results represent improvement and generalization of the previously known results in literature. (c) 2005 Elsevier Ltd. All rights reserved.
mixed quasi-variational-like inclusion banach space minimax inequality auxiliary variational inequality iterative algorithm