Startseite Mathematik Remarks on w-distances and metric-preserving functions
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Remarks on w-distances and metric-preserving functions

  • Thanakorn Prinyasart und Suchat Samphavat EMAIL logo
Veröffentlicht/Copyright: 15. Februar 2023
Veröffentlichen auch Sie bei De Gruyter Brill

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/S207004662103002XSuche in Google Scholar

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

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

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

[6] Imdad, M.—Rouzkard, F.: Fixed point theorems in ordered metric spaces via w-distances, Fixed Point Theory Appl. (2012), 2012:222.10.1186/1687-1812-2012-222Suche 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/s13398-020-00891-7Suche 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.Suche 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-2017-0163Suche 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.Suche 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.Suche in Google Scholar

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

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

[14] Pongsriiam, P.—Termwuttipong, I.: Remarks on ultrametrics and metric-preserving functions, Abstr. Appl. Anal. (2014), Art. ID 163258.10.1186/1687-1812-2014-179Suche 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-2017-0331Suche in Google Scholar

[16] Takahashi, W.: Nonlinear Functional Analysis. Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, 2000.Suche 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-2017-0476Suche in Google Scholar

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

Artikel in diesem Heft

  1. RNDr. Stanislav Jakubec, DrSc. passed away
  2. Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means
  3. Conditions forcing the existence of relative complements in lattices and posets
  4. Radically principal MV-algebras
  5. A topological duality for dcpos
  6. Padovan or Perrin numbers that are concatenations of two distinct base b repdigits
  7. Addendum to “A generalization of a result on the sum of element orders of a finite group”
  8. Remarks on w-distances and metric-preserving functions
  9. Solution of logarithmic coefficients conjectures for some classes of convex functions
  10. Multiple periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian and partially periodic potentials
  11. Asymptotic stability of nonlinear neutral delay integro-differential equations
  12. On Catalan ideal convergent sequence spaces via fuzzy norm
  13. Fourier transform inversion: Bounded variation, polynomial growth, Henstock–Stieltjes integration
  14. (ε, A)-approximate numerical radius orthogonality and numerical radius derivative
  15. Wg-Drazin-star operator and its dual
  16. On the Lupaş q-transform of unbounded functions
  17. K-contact and (k, μ)-contact metric as a generalized η-Ricci soliton
  18. Compactness with ideals
  19. Number of cells containing a given number of particles in a generalized allocation scheme
  20. A new generalization of Nadarajah-Haghighi distribution with application to cancer and COVID-19 deaths data
  21. Compressive sensing using extropy measures of ranked set sampling
  22. A note on star partial order preservers on the set of all variance-covariance matrices
Heruntergeladen am 16.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2023-0008/pdf?lang=de
Button zum nach oben scrollen