Functions that preserve the weak ultrametric and implications.
Abstract
Previously, we presented the current state of the family of functions that preserve the weak ultrametric UD and of the set of functions that preserve the extended b–metric BE and its relationship with existing ones. In this paper we continue with the investigation providing some equivalences or characterizations for the set of functions that preserve the weak ultrametric UD, and this fact implies that, the graph of the elements in UD is contained in the region proposed by J. Dobos and Z. Piotrowski.
Downloads
References
Bakhtin, I. A. (1989). The contraction mapping principle in almost metric space. Functional Analysis, 30:26–37.
Corazza, P. (1999). Introduction to metric-preserving functions. The American Mathematical Monthly, 106(4):309–323.
Dobous, J. (1997). When distance mean money. International Journal of Mathematical Education in Science and Technology, 28(4):513–518.
Dobous, J. (1998). Metric Preserving Functions. Online Lecture Notes available at http://web,science.upjs.sk/jozefdobos/wpcontent/uploads/2012/03/mpf1.pdf.
Kamran, T., Samreen, M., and UL Ain, Q. (2017). A generalization of b–metric space and some fixed point theorems. Mathematics, 5(2):1–7.
Khemaratchatakumthorn, T. and Pongsriiam, P. (2018). Remarks on b–metric and metric-preserving functions. Mathematica Slovaca, 68(5):1009–1016.
Khemaratchatakumthorn, T. and Pongsriiam, P. (2019). Further remarks on b–metrics, metric-preserving functions, and other related metrics. International Journal of Mathematics and Computer Science, 14(2):473–480.
Martínez, Cruz Reinaldo y Hernández, P. E. (2022). Funciones que preservan la b–métrica extendida y otras métricas relacionadas. Padi Boletín Científico De Ciencias Básicas de Ingeniería Del ICBI, Publicación Semestral, 9:47–55.
P. Fraigniaud, E. Lebhar, L. V. (2008). The inframetric model for the internet. IEEE INFOCOM-The 27th Conference on Computer Communications Societies, pages 13–18.
Pongsriiam, P. and Termwuttipong, I. (2014). Remarks on ultrametrics y metric-preserving functions. Abstract and Applied Analysis, 2014:1–9.
Siegfried, B., Guntzer, U., and Remmert, R. (1984). Non-Archimedean Analysis. Grundlehren der Mathematischen Wissenschaften, Springer.
Yurova, E. (2013). On ergodicity of p-adic dynamical systems for arbitrary prime p. P-Adic Numbers, Ultrametric Analysis, and Applications, pages 239–241.
Copyright (c) 2024 Reinaldo Martínez-Cruz
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
