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arXiv:2308.01003 [math.GN]AbstractReferencesReviewsResources

Fixed point theorem for mappings contracting perimeters of triangles

Evgeniy Petrov

Published 2023-08-02Version 1

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.

Comments: 8 pages, 1 figure, A full-text view-only version is available online at https://rdcu.be/dijGN
Journal: J. Fixed Point Theory Appl. 25, 74 (2023)
Categories: math.GN
Subjects: 47H10, 47H09
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