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