广义膨胀映射的不动点定理

<正> 最近,文章1]对应于压缩映射引入了三类膨胀映射,在完备的度量空间上,给出了它们的不动点定理。本文将对应于2]、3]引入几类更广义的臌胀映射及其膨胀映射对,并给出相应的不动点定理。其中某些定理扩广了1]中的一些结果。 定义1 设X=(X,d)是度量空间,T_1,T_2,T是X上的自映射。若存在常数L>1和映射n,m:X→I~+(自然数集).(?)x,y∈X成立下式:

Fixed point theorems of generalized expanding mappings

In this paper, generalized expanding mappings of several types are intro-duced. On complete metric space with distance function d, theirfixed point theorems are obtained and some results in 1 ] are extended.