ω-连通空间上弱Φ-映射族的不动点,重合点和聚合不动点

Fixed Points,Coincidence Points and Collectively Fixed Points for Weak Φ-Maps on ω-Connected Spaces

利用广义凸空间上的Fan-Browder型不动点定理得到若个干新的在没有任何凸结构和线性结构及紧性框架的ω-连通空间上的弱Φ-映射的不动点定理.作为应用,根据ω-连通空间上得到的Fan-Browder型不动点定理讨论了两个弱Φ-映射的重合点存在性问题和一族弱Φ-映射的聚合不动点的存在性问题.所得结果推广和改进了文献中的相应结论.

We use Fan-Browder type fixed point theorem on generalized convex spaces to obtain some new fixed point theorems for weak φ-maps on ω-connected spaces without any convex and linear structure and compact framework. As applications, using the obtained Fan-Browder type fixed point theorem on ω-connected spaces, we discuss the existence problems of coincidence points for two weak φ-mappings and collectively fixed points for a family of weak O-mappings. The obtained results generalize and improve the corresponding conclusions in references.