广义集压缩映射组的不动点和最佳逼近

FIXED POINT AND BEST APPROXIMATION FOR A SYSTEM OF GENERALIZED SET-CONTRACTION MAPPINGS

本文对Ｂａｎａｃｈ空间中多元映射组引入了广义集压缩映射组概念，证明了某些不动点定理和最佳逼近定理。这些定理分别改进和推广了Ｄａｒｂｏ定理，Ｋｒａｓｎｏｓｅｌｓｋｉｉ定理，Ｓｃｈａｅｆｅｒ定理和ＫｙＦａｎ的最佳逼近定理。

In this paper,we introduce the concept of a system of generalized set-contractive mappings in Banach spaces,prove some fixed point theorems and the best approximation theorem for the system.Our results improve and generalize Darbo's,Krasnoselskii's,Schaefer's theorem and the best approximation theorem of Ky Fan's type.