完备度量空间上的不动点定理

1922年,Banach证明了压缩映射的不动点的存在性。不动点理论对于解决一些实际问题诸如代数方程、微分方程、积分方程中都有应用。B ranc iari1]提出了完备度量空间上的边值压缩,并证明了边值压缩映射的不动点定理。本文给出了完备度量空间上的三个不动点定理,推广了B ranc iari1]中的结果,并且举例说明本文的结果是对Banach压缩定理的推广。

Fixed point theorems in a complete metric space

In 1922,Banach proved the existence of fixed point for contraction mapping.Fixed point theory plays a important role in many problems such as algebra equation,differential equation and integral equation.Branciari provided edge contraction and gave the fixed point theorems for edge contraction mapping in complete metric space.In this paper,three fixed point theorems which are the generalizations of the Banach Contraction Principle are proved in a complete metric space.And one example is given to show that our results extend Banach Contraction Principle.