The Research Into The Existence Of The Solutions Of A New System Of Generalized Mixed Quasi-Variational-Like Inclusions Problems

In this thesis, a new system of generalized mixed quasi-variational-like inclusions problems are studied. First, by means of theoretic algorithm, the existence of the solutions of the problems in q—uniformly smooth Banach spaces are discussed. And, by strengthening the set-valued mappings, we can get properties of the solution set, which does not depend on theoretic algorithm. Then, the existence and uniqueness of the solutions of the problems are studied. Finally, we raise a new system of generalized variational-like inequalities problems. By using auxiliary problems, we can construct an algorithm for the system of variational inequalities problems. Furthermore, we prove the existence of the solutions of the problems and discuss the convergence analysis of the algorithm.