度量空间上具有Lipschitz条件的集值映射族的公共不动点

摘要

在完备的度量空间上,通过构造收敛序列,得到满足Lipschitz条件的集值映射族的公共不动点的存在定理,并证明在较强的条件下公共不动点是唯一的,同时给出若干个特殊结果.所得结果表明,Lipschitz条件中的系数之和可以大于或等于1.推广和改进了很多这种类型的公共不动点定理.%In a complete metric space,by constructing convergent sequences,the existence of common fixed point for the family of set valued mappings satisfying Lipschitz conditions is proven,and further it is proven that the common fixed point is unique under stronger conditions.Several special results are obtained,which shows that the sum of the coefficients in Lipschitz condition may be greater than or equal to 1.This generalizes and improves many common fixed point theorems of this type.