广义凸空间上重合点定理,几乎不动点定理和不动点定理

Coincidence Point Theorems,Almost Fixed Point Theorems,Fixed Point Theorems on Generalized Convex Spaces

引进了广义凸空间上关于某一映射的广义S-KKM映射和广义W-S-KKM映射的概念,得到了广义凸空间上的连续选择定理和Fan-Browder型不动点定理并给出两个φ-映射的重合点存在定理.最后,讨论了具有S-KKM性质或具有W-S-KKM性质的映射的几乎不动点和不动点的存在问题.所的结论推广和改进了一些已有的结果.

The concepts of a generalized S-KKM map and a generalized W-S-KKM map with respect to another map on generalized convex spaces are introduced,continuous selection theorems and Fan-Browder type fixed point theorems are also obtained in this space,and from which,the existence theorems of coincidence points for two Φ-maps are given.Finally,the existence problems of almost fixed points and fixed points for maps with S-KKM property or W-S-KKM property are discussed.The obtained results generalize and improve many known conclusions.