The renorming technique allows one to apply the Banach Contraction Principle for maps which are not contractions with respect to the original metric. This method was invented by Bielecki and manifested in an extremely elegant proof of the Global Existence and Uniqueness Theorem for ODEs. The present paper provides further extensions and applications of Bielecki’s method to problems stemming from functional analysis and from the theory of functional equations.

中文翻译：

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Bielecki重命名技术的应用

重新规范化技术允许将“ Banach收缩原理”应用于相对于原始度量而言不是收缩的地图。这种方法是由Bielecki发明的，并在ODE的整体存在性和唯一性定理的极其优雅的证明中得到体现。本文提供了Bielecki方法的进一步扩展和应用，以解决源自泛函分析和泛函方程理论的问题。