完备凸度量空间中(次)相容和集值广义非扩张映象的公共不动点定理

Common Fixed Point Theorems for (sub) Compatible and Set-Valued Generalized Nonexpansive Mappings inComplete Convex Metric Spaces

本文在完备凸度量空间中,利用集值和单值映象(次)相容的一些条件,建立了数值广义非扩张映象存在公共不动点的一个充要条件和一个充分条件.我们的结果改进、扩充和发展了文[2～7]中的主要结果.

In this paper, using some conditions of (sub) compatibility between a set-valued mapping and a single-valued mapping, we establish a necessary and sufficient rendition and a sufficient condition for set-valued generalized nonexpansive mappings to have a unique common fixed point in complete convex metric spaces. Our results improve, extend and develop the main results in [2-7].