局部FC-一致空间内的广义拟变分包含组及其应用(Ⅰ)(英文)  

Systems of Generalized Quasi-Variational Inclusions in Locally FC-Uniform Spaces and Applications(I)

作　　者：丁协平[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2009年第4期411-420,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省教育厅自然科学重点研究基金(07ZA092,SZD0406)资助项目~~

摘　　要：在局部FC-一致空间内引入和研究了某些新的广义拟变分包含组和联立广义拟变分包含组.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,在局部FC-一致空间内对广义拟变分包含组和联立广义拟变分包含组的解证明了某些新的存在性定理.这些结果在较弱的假设下将文献中很多已知结果从局部凸拓朴矢量空间的闭凸子集推广到没有凸性结构的局部FC-一致空间.这些结果的某些应用,将在一篇后继文章中给出.In this paper, we introduce and study some new classes of systems of generalized quasi-variational inclusion problems and simultaneous generalized quasi-variational inclusion problems in locally FC-uniform spaces. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some new existence theorems of solutions for the system of generalized quasi-variational inclusion problems and the system of simultane- ous generalized quasi-variational inclusion problems are proved in locally FC-uniform spaces. These results improve and generalize many known results in literature from closed convex subsets of locally convex topological vector spaces to locally FC-uniform spaces without convexity structure under weaker assumptions. Some applications of these results will be given in follow-up papers.

关 键 词：不动点 (联立)广义拟变分包含问题组 pi-FC-部分对角拟凸 FC-部分对角拟凸 局部FC-一致空间 

分 类 号：O177.92[理学—数学]