Extended b-metric-preserving functions

TL;DR

This paper introduces new classes of functions called DU and EB, explores their relationships with existing classes, and characterizes their properties and graphical regions within the context of b-metric-preserving functions.

Contribution

It defines the classes DU and EB, establishes their properties, and relates them to known function classes and graphical regions, advancing the understanding of b-metric-preserving functions.

Findings

EB functions are amenable and quasi-subadditive.

The graph of EB functions lies within a specific region by Dobos and Piotrowski.

Relationships between DU, EB, and other known classes are clarified.

Abstract

In this paper, we introduce a couple of classes of functions, denoted by DU and EB. We present the relationship between them and other known classes. Also, we show that the elements of the class EB, are amenable and quasi-subadditive functions (Theorem 2.14). Finally, in the Theorem 2.20, we establish that the graphic of these elements is contained in the region proposed by J. Dobos and Z. Piotrowski(see [8]).