Funciones que preservan la ultramétrica débil e implicaciones

Reinaldo Martínez-Cruz; Marian Citlalli Cruz-Cruz; José Erasmo Pérez-Vázquez; Ricardo López-Hernández

doi:10.29057/icbi.v11i22.11090

Authors

Reinaldo Martínez-Cruz Universidad Autónoma de Tlaxcala | Tlaxcala | México. https://orcid.org/0000-0001-7516-6943
Marian Citlalli Cruz-Cruz Universidad Autónoma de Tlaxcala | Tlaxcala | México. https://orcid.org/0009-0005-6336-1182
José Erasmo Pérez-Vázquez Universidad Autónoma de Tlaxcala | Tlaxcala | México. https://orcid.org/0000-0002-6702-5312
Ricardo López-Hernández Universidad Autónoma de Tlaxcala | Tlaxcala | México. https://orcid.org/0000-0002-8580-3632

DOI:

https://doi.org/10.29057/icbi.v11i22.11090

Keywords:

Ultrametric, weak ultrametric, extended b-metric

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

Download data is not yet available.

Publication Facts

This article

Author statements

Data availability

N/A

16%

External funding

No

32%

Competing interests

N/A

11%

This journal

Other journals

Articles accepted

86%

33%

Days to publication

248

145

Indexed in

GS

Editor & editorial board: profiles
Academic society: N/A
Publisher: Universidad Autónoma del Estado de Hidalgo

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.