Fixed point theorem for mappings contracting perimeters of triangles

By E. Petrov. Journal of Fixed Point Theory and Applications, 2023

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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. Examples of mappings contracting perimeters of triangles which are not contraction mappings are constructed.

Subfields: Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/37e0ec2f865cc0e63f85abe07ca435ad0018a914