The Solvability Of Perturbed Variational Inequalities

In this dissertation, we mainly study the existence of some classes variational inequalities by perturbation. We introduce two perturbed ways for mappings: one says it is perturbed by a nonlinear mapping,and the other says it is perturbed by a vector. The full text is divided into five chapters. We introduce them as follows:In the first chapter, we introduce the research background and basic definitions and con-cepts herein.In the second chapter, we introduce the definitions of sum of a fuzzy mapping and a nonlinear mapping, the sum of a fuzzy mapping and a vector, and the scalar multiplication of a fuzzy mapping, respectively. They may be used to characterize the perturbation of a fuzzy mapping. Moreover,we prove that the perturbed variational inequality with a fuzzy mapping perturbed by two ways (a nonlinear mapping and a vector,resp.) has a solution.In the third chapter, we investigate the existence of a generalized mixed variational in-equality perturbed by two ways.In the fourth chapter, we study the perturbation of generalized variational inequalities is introduced in reflexive Banach space. When the constrained set is weakly compact, we deduce an existence theorem for generalized variational inequalities. Employing this result,the aim of this chapter is to establish existence results for some variational-like inequalities by a nonlinear mapping. Meanwhile, we show that there is a solution of generalized variational inequalities in a bounded set.In the last chapter, we summarize our work in this dissertation and suggest some possible future work.