Extended b-metric preserving functions

In a previous investigation, we present the current state of the family of functions that preserve the weak ultrametric UD and the set of maps that preserve the extended b–metric BE and their relation to those existing in the literature. In this article, we continue with the investigation by providing a characterization for the space BE, and this fact allows us to verify that the graph of the elements in BE are found in the region proposed by J. Doboš and Z. Piotrowski. Furthermore, we generalize some results from Tammatada Khemaratchatakumthorn, Prapanpong Pongsriiam and Suchat Samphavat.