Banach压缩映象原理与空间完备性

Banach Contraction Principle and Completeness

本文进一步揭示了Ｂａｎａｃｈ压缩映象原理与完备性的关系，指出：一般地，Ｂａｎａｃｈ压缩映象原理等价于道路完备性，在一定条件下才等价于完备性。

In this paper, a new result for completeness and Banach contraction principle is obtained. We prove that Banach contraction principle is equivalent to the path completeness, and we also give a necessary and sufficient condition which grarantees the equivalence of completeness and Banach contraction principle.