English

Fixed point theorem for mappings contracting perimeters of triangles

General Topology 2023-08-03 v1

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.

Keywords

Cite

@article{arxiv.2308.01003,
  title  = {Fixed point theorem for mappings contracting perimeters of triangles},
  author = {Evgeniy Petrov},
  journal= {arXiv preprint arXiv:2308.01003},
  year   = {2023}
}

Comments

8 pages, 1 figure, A full-text view-only version is available online at https://rdcu.be/dijGN

R2 v1 2026-06-28T11:46:13.758Z