Fixed point theorem for mappings contracting perimeters of triangles
arXiv:2308.01003 · doi:10.1007/s11784-023-01078-4
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.
8 pages, 1 figure, A full-text view-only version is available online at https://rdcu.be/dijGN
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