On functions preserving products of certain classes of semimetric spaces

Abstract

In the paper we continue the research of Borsík and Doboš on functions which allow us to introduce a metric to the product of metric spaces. In this paper we extend their scope on broader class of spaces which usually fail to satisfy the triangle inequality, albeit they tend to satisfy some weaker form of this axiom. In particular, we examine the behavior of functions preserving b-metric inequality. We provide analogues of the results of Borsík and Doboš, adjusted to the new, broader setting. The results we obtained are illustrated with multitude of examples. Furthermore, the connections of newly introduced families of functions with the ones already known from the literature are investigated.

Applications of ball spaces theory: fixed point theorems in semimetric spaces and ball convergence

“…Since semimetric spaces, that is, spaces with distance function which does not have to satisfy the triangle inequality, occurred to be important in application for example in IT (e.g. see the section Applications in [12]), also fixed point theorems in such spaces became important. This topic was investigated for example in [2,3,6,14,15].…”