On characterization of functions preserving metric-type conditions via triangular and polygonal structures

TL;DR

This paper extends the characterization of functions that preserve metric-like properties using triangle triplets, generalizes sum lemmas for broader metric-type spaces, and introduces methods to generate non-metric strong b-metric spaces.

Contribution

It develops more general analogues of sum lemmas for metric-type spaces and extends existing theorems on property-preserving functions using triangle triplets.

Findings

Extended sum lemmas for broader classes of metric-type spaces

Generalized characterizations of property-preserving functions

Methods to generate non-metric strong b-metric spaces

Abstract

Following the train of thought from our previous paper we revisit the theorems of Pongsriiam and Termwuttipong by further developing their characterization of certain property-preserving functions using the so-called triangle triplets. We develop more general analogues of disjoint sum lemmas for broader classes of metric-type spaces and we apply these to extend results of Bors\`ik an Dobo\v{s} as well as those obtained by Khemaratchatakumthorn and Pongsriiam. As a byproduct we obtain methods of generating non-trivial and infinite strong $b$-metric spaces which are not metric.