Fixed point theorem for mappings contracting perimeters of triangles

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

Cited by in corpus (2)

• On generalizations of some fixed point theorems in semimetric spaces with triangle functions
• Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points