Remetrization techniques for mappings contracting perimeters of triangles - Ćvetković, Marija (Nonlinear Analysis: Modelling and Control, 2026)
There exists a metric in which a mapping contracting perimeters of triangles becomes a graphic contraction, while the completeness of the underlying space is preserved. The reverse question is also considered. We discuss in which cases those two metrics are equivalent and obtain some stability results of the fixed point problem with respect to the original metric and the induced one. The theory is substantiated with numerous examples and a discussion on the advantages regarding the scope of applications.