On ultrametrics, b-metrics, w-distances, metric-preserving functions, and fixed point theorems

Abstract

In this article, new classes of functions based on new variations of metric-preserving functions are defined. Necessary and sufficient conditions for functions to be in these classes are also provided. As a result, we can explain relations between all classes and learn that all functions in the classes are weakly separated from 0. We can extend fixed point theorems, which were originally provided by Kirk and Shahzad and were later extended by Pongsriiam and Termwuttipong, in this journal by considering all functions that are weakly separated from 0.