Abstract
The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u∈U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.