Abstract

The Banach Contraction Mapping Principle has many generalizations and extensions in different directions. Here we define \((\varepsilon,\psi)\)-Uniformly Local Weak Contractions and show that these mappings admit unique fixed points. We obtain a generalization of two existing results. We construct an example which illustrates of our main result in which the mapping is neither a \(\psi\)-weak contraction nor a local contraction.

中文翻译：

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收缩映射原理的局部弱版本

摘要

Banach 收缩映射原理在不同方向上有许多概括和扩展。这里我们定义了\((\varepsilon,\psi)\) -Uniformly Local Weak Contractions 并表明这些映射允许唯一的不动点。我们获得了两个现有结果的概括。我们构建了一个例子来说明我们的主要结果，其中映射既不是\(\psi\) -弱收缩也不是局部收缩。