Boyd和Wong映象与Banach压缩映象原理的等价性

Equivalence Between Boyd and Wong's Fixed Piont Theorem And Banach's Contraction Mapping Principle

给出了Boyd和Wong映象不动点定理与Banach压缩映象原理在两个相当弱的条件下的等价性,Banach压缩映象原理在理论及应用上的优点是众所周知的,因此,压缩映射等价性的研究在数学理论上有着极其重要的作用。

If the space is compact one or the function is monotone non-decreasing,the equivalence between Boyd and Wong's fixed point theorem and Banach's contraction mapping principle is proved.As we all know, Banach's contraction mapping principle is very important in theory and application, so the research of equivalence between the two principle is important too.