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<p>We consider a new type of mappings in metric spaces termed mappings contracting the total pairwise distances between <i>n</i> points. It is shown that these mappings are continuous. A theorem on the existence of periodic points for these mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary as well as the fixed-point theorem for mappings contracting perimeters of triangles. Examples of mappings contracting the total pairwise distances between <i>n</i> points and having different properties are constructed.</p>

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Periodic points of mappings contracting total pairwise distances

  • 期刊论文

  • 发表日期：

    2025年3月28日

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  • Evgeniy Petrov

摘要

We consider a new type of mappings in metric spaces termed mappings contracting the total pairwise distances between n points. It is shown that these mappings are continuous. A theorem on the existence of periodic points for these mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary as well as the fixed-point theorem for mappings contracting perimeters of triangles. Examples of mappings contracting the total pairwise distances between n points and having different properties are constructed.