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Remarks on w-distances and metric-preserving functions

  • Thanakorn Prinyasart and Suchat Samphavat EMAIL logo
Published/Copyright: February 15, 2023
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Abstract

In this paper, we define new classes of functions related to metrics and w-distances. We also provide characterizations of functions in these classes. As a consequence, we obtain relations between all classes.

Acknowledgement

The authors wish to thank Jittisak Rakbud for a discussion that gives rise to an idea of studying Section 3.5. We would also like to thank anonymous reviewers for valuable and constructive comments and suggestions.

References

[1] Bilet, V.—Dovgoshey, O.—Shanin, R.: Ultrametric preserving functions and weak similarities of ultrametric spaces, p-Adic Numbers Ultrametric Anal. Appl. 13(3) (2021), 186–203.10.1134/S207004662103002XSearch in Google Scholar

[2] Borsík, J.—Doboš, J.: Functions whose composition with every metric is a metric, Math. Slovaca 31 (1981), 3–12.Search in Google Scholar

[3] Corazza, P.: Introduction to metric-preserving functions, Amer. Math. Monthly 106(4) (1999), 309–323.10.1080/00029890.1999.12005048Search in Google Scholar

[4] Doboš, J.: Metric Preserving Functions, Online Lecture Notes; available at http://web.science.upjs.sk/jozefdobos/wp-content/uploads/2012/03/mpf1.pdfSearch in Google Scholar

[5] Dovgoshey, O.: On ultrametric-preserving functions, Math. Slovaca 70(1) (2020), 173–182.10.1515/ms-2017-0342Search in Google Scholar

[6] Imdad, M.—Rouzkard, F.: Fixed point theorems in ordered metric spaces via w-distances, Fixed Point Theory Appl. (2012), 2012:222.10.1186/1687-1812-2012-222Search in Google Scholar

[7] Jachymski, J.—Turoboś, F.: On functions preserving regular semimetrics and quasimetrics satisfying the relaxed polygonal inequality, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), Art. No. 159.10.1007/s13398-020-00891-7Search in Google Scholar

[8] Kada, O.—Suzuki, T.—Takahashi, W.: Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Mathematica Japonica 44(2) (1996), 381–391.Search in Google Scholar

[9] Khemaratchatakumthorn, T.—Pongsriiam, P.: Remarks on b-metric and metric-preserving functions, Math. Slovaca 68(5) (2018), 1009–1016.10.1515/ms-2017-0163Search in Google Scholar

[10] Khemaratchatakumthorn, T.—Pongsriiam, P.—Samphavat, S.: Further remarks on b-metrics, metric-preserving functions, and other related metrics, Int. J. Math. Comput. Sci. 14(2) (2019), 473–480.Search in Google Scholar

[11] Khemaratchatakumthorn, T.—Termwuttipong, I.: Metric-preserving functions, w-distances and Cauchy w-distances, Thai J. Math. 5(3) (2007), 51–56.Search in Google Scholar

[12] Pokorný, I.: Some remarks on metric preserving functions, Tatra Mt. Math. Publ. 2 (1993), 65–68.Search in Google Scholar

[13] Pongsriiam, P.—Termwuttipong, I.: On metric-preserving functions and fixed point theorems, Fixed Point Theory Appl. (2014), 2014: 179.Search in Google Scholar

[14] Pongsriiam, P.—Termwuttipong, I.: Remarks on ultrametrics and metric-preserving functions, Abstr. Appl. Anal. (2014), Art. ID 163258.10.1186/1687-1812-2014-179Search in Google Scholar

[15] Samphavat, S.—Khemaratchatakumthorn, T.—Pongsriiam, P.: Remarks on b-metrics, ultrametrics and metric-preserving functions, Math. Slovaca 70(1) (2020), 61–70.10.1515/ms-2017-0331Search in Google Scholar

[16] Takahashi, W.: Nonlinear Functional Analysis. Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, 2000.Search in Google Scholar

[17] Vallin, R. W.—Dovgoshey, O. A.: P-adic metric preserving functions and their analogues, Math. Slovaca 71(2) (2021), 391–40810.1515/ms-2017-0476Search in Google Scholar

[18] Wilson, W. A.: On certain types of continuous transformations of metric spaces, Amer. J. Math. 57(1) (1935), 62–68.10.2307/2372019Search in Google Scholar

Received: 2021-06-28
Accepted: 2021-12-31
Published Online: 2023-02-15
Published in Print: 2023-02-23

© 2023 Mathematical Institute Slovak Academy of Sciences

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