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arXiv · 2402.02536

Periodic points of mappings contracting total pairwise distance

Evgeniy Petrov
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Abstract

We consider a new type of mappings in metric spaces so-called mappings contracting total pairwise distance on $n$ points. It is shown that such mappings are continuous. A theorem on the existence of periodic points for such 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 total pairwise distance on $n$ points and having different properties are constructed.

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Evgeniy Petrov. 2024-02-04. Periodic points of mappings contracting total pairwise distance. https://doi.org/10.1007/s11784-025-01190-7

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