第(m)类Lipschitz映象的不动点定理

Fixed Point Theorems For m—th—Type Lipschitz Mappings

本文在距离空间中引入了第(m)类,m=1,2,…,7,Lipschitz映象的概念,并且给出了这些映象具有不动点的充要条件或充分条件.这样,众多分散的压缩映象、非扩张映象,甚至通常意义的Lipschitz映象和"Holder映象",都可以作为特例而统一纳入第(m)类Lipschitz映象去加以研究。

In this paper m—th—Lipschitz mappings, which develop from more general view the concept of the Lipschitz mappings in the ordinary sense, are introduced. Some theorems for the fixed point existences of m—th—Lipschitz mappings are given. Thus the conditions of existences for the fixed point of the relative nonexpansive mappings are obtained.