局部FC-一致空间内凝聚映象的极大元和广义对策及应用(Ⅰ)

首先在没有凸性结构的局部FC-一致空间内引入了非紧性测度和凝聚集值映象概念.在局部FC-一致空间内对涉及凝聚集值映象的集值映象族证明了新的极大元存在性定理.作为应用,在局部FC-一致空间内对涉及凝聚集值映象的广义对策建立了某些新的平衡存在性定理.这些结果改进和推广了文献中的某些已知结果到局部FC-一致空间.对广义矢量拟平衡组的进一步应用,我们将在文(Ⅱ)中给出.

Maximal Elements and Generalized Games Involving Condensing Mappings in Locally FC-Uniform Spaces and Applications(Ⅰ)

First,the notions of the measure of noncompactness and condensing set-valued mappings were introduced in locally FCuniform spaces without convexity structure.A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings was proved in locally FC-uniform spaces.As applications,some new equilibrium existence theorems of generalized game involving condensing mappings were established in locally FC-uniform spaces.These results improve and generalize some known results in literature to locally FC-uniform spaces.Some further applications of the results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.