Existence And Iterative Algorithms For Mixed Quasi-variational-like Inequalities

In this paper,a new class of mixed quasi-variational-like inequalities in reflexive Banach spaces is introduced and investigated.By applying a minimax inequality due to Ding-Tan and a lemma due to Chang,some existence and uniqueness results of solution for the mixed quasi-variational-like inequality are established.Next,by using a KKM theorem due to Fan and an auxiliary principle technique due to Cohen,two iterative algorithms and the convergence criteria of iterative sequences generated by the iterative algorithms are suggested.The results extend,improve and unify several known results in the literature.