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. We extend their scope to a 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

“…spaces with a distance function which does not have to satisfy the triangle inequality, turned out to be important in applications for example in computer science (e.g. see the section Applications in [16]), also fixed point theorems in such spaces became important. This topic was investigated for example in [2,5,8,18,19].…”