度量凸空间上具有唯一公共不动点的非自集值映射族

A Family of Non-self Multi-valued Mappings Having an Unique Common Fixed Point on Metrically Convex Spaces

在完备的度量凸空间框架下,给出了若干个满足某种Lipschitz条件和边界条件的非自集值映射族的唯一公共不动点的存在性定理.同时讨论了相对单值映射族的更一般形式的公共不动点问题.所得结果推广和改进了许多压缩型单值或集值映射族的公共不动点定理.

Some existence theorems of unique common fixed points for a family of non-self multi-valued mappings satisfying some Lipschitz type condition and boundary condition in a metrically convex space are given. And more general common fixed point problems for non-self single valued mappings are discussed. Our main theorems generalize and improve many common fixed point theorems for a family of single valued or multi-valued mappings of contractive type.