Research On Several Kinds Of Variational Inequalities And Variational Inclusions

Variational inequality theory originated in mechanics and non-linear programming problem, it had a wide application on the realms of engineering, economics and control theory etc. First, the thesis introduced the development course of variational inequalities, then the thesis aimed at some different kinds of variational inequalities and variational inclusions, the existence of solutions was proved by using different methods.The main contents were as follows:1. The existence of solutions for a class of generalized set-valued quasi-variational inclusions and a system of variational inclusions was proved by using the resolvent operator in real reflexive Banach space.2. A class of systems of stochastic generalized strongly nonlinear quasi-variational inequalities was studied. The existence of solutions and the convergence of iterative measurable function sequences produced by new iterative algorithms were proved by using the projection operator in real Hilbert space.3. The existence of solutions and the convergence of iterative sequences for a class of nonlinear set-valued fuzzy variational inequalities and a system of nonlinear set-valued fuzzy variational inequalities were proved by using auxiliary principle in real reflexive Banach space.The acquired results were the unity, improvement and promotion for the relevant existing results.