The Stability Of Solution Set To η-set-valued Weak Vector Variational Inequality Problem

The variational inequality problem is an important part in the linear analysis andget more and more attention. With the theory of variational inequalities graduallymatured. variational inequalities is also gradually introduced by optimizationtheory,game theory and so on. As the classical variational inequality theory developedrapidly, the researchers began to promote variational inequality from "quantity" to"vector" value, and joined the special structure (coherent structure), and maintain theoriginal form of classical variational inequality. The vector variational inequalityproblem was originally introduced in finite dimensional space. Then, the vectorvariational inequality in finite dimensional space was promoted to the infinitedimensional space. Now, we have more and more research about this problem and geta lot of proof for the existence of a solution in variational inequality study. Anotherimportant research direction of the vector variational inequality is stability. We allknow that Semi-continuous operator weaker than continuity. So under the condition ofv-semicontinuous, the study of stability of the set-valued weak vector variationalinequality problem is rare. Therefore under the condition of v-semicontinuous, it ismeaningful to study the set-valued weak vector variational inequality.The main contents are as follows: First, describe the evolution of variationalinequalities, while introduce its research background and research status briefly forhave a macro understanding. Secondly, the set-value weak vector inequality problemextended to a wider range of model,η-set-valued the value weak vector variationalinequality problem. And introduce the concept of invariant convex set to the model.Thirdly, under the assumption of weak C pseudomonotonous, semi-continuousoperator, we study the solution ofη-set-valued the value weak vector variationalinequality problem and its upper semi-continuity. This part is the core part of the paper. Finally summarizes the Solution Set toη-Set-valued Weak Vector VariationalInequality Problem. There are many sections to do aboutη-Set-valued weak vectorvariational inequality problem.