FC-空间内广义拟变分关系问题组及其应用(英文)

System of Generalized Quasi-Variational Relation Problems inFC-Spaces and Applications

在没有凸性结构的FC-空间内引入和研究了一类新的广义拟变分关系问题组.由使用作者对集值映像建立的极大元存在性定理,在非紧FC-空间内对广义拟变分关系问题组的解证明了某些新的存在性定理.作为应用,在相当温和的假设下得到了集值映像族的新的拟-KKM型定理,具有模糊约束的约束矢量Nash平衡问题和广义拟变分包含问题解的新的存在性结果.

In this paper, new systems of generalized quasi-variational relation problems are introduced and studied in FC-spaces without convexity structure. By applying an existence theorem of maximal elements of set-val- ued mappings due to author, some new existence theorems of solutions for the systems of generalized quasi-varia- tional relation problems are proved in noncompact FC-spaces. As applications, some new quasi - KKM type theo- reins for a family set-valued mappings and some new existence results of solutions for constraint vector Nash equilib- rium problem with fuzzy constraints and systems of generalized quasi-variational inclusion problems are obtained un- der quite mild conditions.