Studies Of Systems Of Variational Inequalities And Variational Inclusions

The purpose of this paper is to obtain the solutions of various types of systems of variational inequalities and variational inclusions by using different methods.The results are the newest inclusions of relative problems,and unify,improve and generalize many known results.In the third section,a new system of generalized quasi-like variational inclusions involving(A,η)- accretive operator is introduced and studied by using the resolvent operator technique of(A,η)- accretive operator.And the existences of solutions and the convergences of sequences produced by the p-step iterative algorithms are proved in real q - uniform smooth Banach space.In the fourth section,using Wiener-Hopf equation technique,a system of variational inequalities involving relaxed co-coceive mappings is discussed.The existences of solutions and the convergences of iterative sequences produced by the iterative algorithms are proved in Hilbert space.In the fifth section,the existence theorem of solutions of a system of variational inequalities is obtained by using penalty operator technique in Hilbert space.In the sixth section,by using auxiliary problem method,the existences of solutions and the convergences of iterative sequences of a new system of generalized set-valued strongly nonlinear mixed variational-like inequalities are proved in two real reflexive Banach spaces.In the seventh section,a new system of generalized mixed set-valued quasi-like variational inclusions with parametric and(H,η)- proximal mapping is introduced and studied in Banach space.A new iterative algorithms are given by using the (H,η)- proximal mapping technique,and the existence and uniqueness of solutions are proved,as well as the convergences of the iterative sequences,and the sensitivity analysis of solutions is studied.