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arXiv · 2308.01003

Fixed point theorem for mappings contracting perimeters of triangles

Evgeniy Petrov
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Abstract

We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary. An example of a mapping contractive perimeters of triangles which is not a contraction mapping is constructed.

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Evgeniy Petrov. 2023-08-02. Fixed point theorem for mappings contracting perimeters of triangles. https://doi.org/10.1007/s11784-023-01078-4

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