Generalized Variational Inequalities Theoretical Research

Ab st r actVariationa1 inequa1 ities problem (VIP) was producedin nineteen sixty four. As an important theory inmathefnatica1 field, it is used in economics' equi l ibriumand so on. In the eight ieth, variational inequa1 ity hasits important development phase and there were suchvari ati ona1 inequa1 it ies as vector vari at ionalinequal ity, general variati ona1 inequal ity quasi-variationa1 inequal ity, 1 ike--variat iona1 inequal ity andgenera1 ized vari at iona1 inequa1 ity. Genera1 izedvariational inequal ity (GVIP) is the extent ion ofvari at iona1 inequal ity. They use the same theory system.So many peop1e such as Brwoder 1 Rocka1la. Saigal' Fang.Ding do the work for the solution to GVIP. In thisd i ssertat ion, there are three points that the writer havedone:First, in the first and second part, writer concludedand summarised ex istence and on ly existence theoryof GVIP. In the third part, writer used the theoryof VIP to GVIP when the function is discontinous.A1so the writer extent some theory of V1P to GVIp.Second, in the forth part, the writer used relationshipin quasi--variat iona1 inequal ity, pseudo-variational inequality and monotone variational inequality and used the solution of monotone GVIP to solute quasi?variational inequality,pseudo?variational inequality. Also some important conclusion were given.Third,in the fifth part, the writer spread the two important conclusions properly and used them to solute GVIP. First it is Ky桭an抯 minmax inequality. Second it is Browder梖ixed point theory.