度量空间上两个自映射公共不动点定理

Common Fixed Point Theorem of Two Self-mappings on Metric Spaces

首先引入一类新的Aφ实函数类的概念,并给出一些例子,然后利用Aφ实函数类,在完备度量空间上建立了一些自映射对的公共不动点定理,如f,g为完备度量空间(X,d)上的两个自映射对,当f,g有一个连续并且存在F∈Aφ使得d(f(x),g(y))≤F(d(x,y),d(x,f(x)),d(y,g(y)))对任意x,y∈X成立,则f,g存在唯一的公共不动点。同时举例说明了本文的结论,统一并推广了文献[5-9]的Reich型压缩映射的不动点定理。

In this paper,first,the concept of a new class of A φ-type real functions,and some examples are given.Next,by using A φ-type real functions,some common fixed point theorems for two self-mappings on complete metric spaces are established.For example,assume（X,d） is a complete metric space,fand gare two self-mappings on X,for gis continuous and there exists F∈ A φ such that d（f（x）,g（y）） ≤F（d（x,y）,d（x,f（x））,d（y,g（y））） for all x,y∈ X,then fand ghave a unique common fixed point in X.Also,an example is given,which show that our results unify and generalize theorems.