On Functions Preserving Products of Certain Classes of Semimetric Spaces

[1] BAKHTIN, I. A.: The contraction mapping principle in almost metric spaces, Functional Analysis 30 (1989), 26–37. (In Russian) Search in Google Scholar

[2] BESSENYEI, M.—PALES, Z.: A contraction principle in semimetric spaces, J. Nonlinear Convex Anal. 18 (2017), 515–524. https://arxiv.org/abs/1401.1709 Search in Google Scholar

[3] BORSÍK, J.—DOBOŠ, J.: Functions whose composition with every metric is a metric, Math. Slovaca 31 (1981), 3–12. http://web.science.upjs.sk/jozefdobos/wp-content/uploads/2012/03/1981b.pdf Search in Google Scholar

[4] BORSÍK, J.—DOBOŠ, J.: On a product of metric spaces, Math. Slovaca 31 (1981), 193–205. http://dml.cz/dmlcz/136266 Search in Google Scholar

[5] BORSÍK, J.—DOBOŠ, J.: On metrization of the uniformity of a product of metric spaces, Math. Slovaca 32 (1982), 97–102. https://dml.cz/handle/10338.dmlcz/130934 Search in Google Scholar

[6] BORSÍK, J.—DOBOŠ, J.: On metric preserving functions, Real Anal. Exchange 13 (1988), 285–293. https://doi.org/10.2307/4415187910.2307/44151879 Search in Google Scholar

[7] CORAZZA, P.: Introduction to metric-preserving functions, Amer. Math. Monthly 106 (1999), no. 4, 309–323. https://doi.org/10.1080/00029890.1999.1200504810.1080/00029890.1999.12005048 Search in Google Scholar

[8] CZERWIK, S.: Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5–11. http://dml.cz/dmlcz/120469 Search in Google Scholar

[9] DAS, P. P.: Metricity preserving transforms, Pattern Recogn. Lett. 10 (1989), 73–76. https://doi.org/10.1016/0167-8655(89)90069-X10.1016/0167-8655(89)90069-X Search in Google Scholar

[10] DOBOŠ, J.: On modifications of the Euclidean metric on reals, Tatra Mt. Math. Publ. 8 (1996), 51–54. Search in Google Scholar

[11] DOBOŠ, J.: Metric preserving functions, (1998). Accessed on September, 1st, 2020: http://web.science.upjs.sk/jozefdobos/wp-content/uploads/2012/03/mpf1.pdf, Search in Google Scholar

[12] DOBOŠ, J.—PIOTROWSKI, Z.: Some remarks on metric preserving functions, Real Anal. Exchange 19 (1994), 317–320. https://doi.org/10.2307/4415384610.2307/44153846 Search in Google Scholar

[13] DOBOŠ, J.—PIOTROWSKI, Z.: A note on metric preserving functions, Int. J. Math. Math. Sci. 19 (1996), 199–200. https://doi.org/10.1155/S016117129600028210.1155/S0161171296000282 Search in Google Scholar

[14] DOBOŠ, J.—PIOTROWSKI, Z.: When distance means money, Internat. J. Math. Ed. Sci. Tech. 28 (1997), 513–518. https://doi.org/10.1080/002073997028040510.1080/0020739970280405 Search in Google Scholar

[15] DOVGOSHEY, O.: Combinatorial properties of ultrametrics and generalized ultrametrics, Bull. Belg. Math. Soc. Simon Stevin 27 (2020), no. 3, 379–417. https://projecteuclid.org/euclid.bbms/159961682110.36045/bbms/1599616821 Search in Google Scholar

[16] DOVGOSHEY, O.: On ultrametric-preserving functions, Math. Slovaca 70 (2020), no. 1, 173–182. https://doi.org/10.1515/ms-2017-034210.1515/ms-2017-0342 Search in Google Scholar

[17] DOVGOSHEY, O.—MARTIO, O.: Products of metric spaces, covering numbers, packing numbers and characterizations of ultrametric spaces, Rev. Roum. Math. Pures Appl. 54 (2009), no. 5–62, 423–439. https://www.csm.ro/reviste/Revue_Mathematique/pdfs/2009/5-6/8Dovgoshey.pdf Search in Google Scholar

[18] FRINK, A. H.: Distance functions and the metrization problem, Bull. Amer. Math. Soc. 43 (1937), 133–142. https://doi.org/10.1090/S0002-9904-1937-06509-810.1090/S0002-9904-1937-06509-8 Search in Google Scholar

[19] HUNG C. C.—CHEN L. H.: A fuzzy TOPSIS decision making model with entropy weight under intuitionistic fuzzy environment. In: Proceedings of the International Multi Conference of Engineers and Computer Scientists 2009 Vol. I. Hong Kong, 2009. pp. 13–16 http://www.iaeng.org/publication/IMECS2009/IMECS2009_pp13-16.pdf Search in Google Scholar

[20] HWANG, C. L.—YOON, K.: Multiple Attribute Decision Making. In: Lecture Notes in Economics and Mathematical Systems Vol. 186. Springer-Verlag, Berlin, 1981. https://link.springer.com/book/10.1007/978-3-642-48318-910.1007/978-3-642-48318-9_3 Search in Google Scholar

[21] JACHYMSKI, J.—MATKOWSKI, J.—SWIĄTKOWSKI, T.: Nonlinear contractions on semimetric spaces, J. Appl. Anal. 1 (1995), 125–134. https://doi.org/10.1515/JAA.1995.12510.1515/JAA.1995.125 Search in Google Scholar

[22] JACHYMSKI, J.—TUROBOŚ, F.: On functions preserving regular semimetrics and quasimetrics satisfying the relaxed polygonal inequality, (RACSAM) Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. Vol. 114, (2020), no. 3, paper no. 159 11 pp. https://doi.org/10.1007/s13398-020-00891-710.1007/s13398-020-00891-7 Search in Google Scholar

[23] JAHANSHAHLOO, G. R.—LOFTI, F. H.—IZADIKHAH, M.: An algorithmic method to extend TOPSIS for decision making problems with interval data, Appl. Math. Comput. 175 (2006), 1375–1384. https://doi.org/10.1016/j.amc.2005.08.04810.1016/j.amc.2005.08.048 Search in Google Scholar

[24] JAHANSHAHLOO, G. R.—LOFTI, F. H.—IZADIKHAH, M.: Extension of the TOPSIS method for decision-making Problems with fuzzy data, Appl. Math. Comput. 181 (2006), 1544–1551. https://doi.org/10.1016/j.amc.2006.02.05710.1016/j.amc.2006.02.057 Search in Google Scholar

[25] JŮZA, M.: A note on complete metric spaces, Matematicko-fyzikálny časopis SAV 6 (1956), 143–148. Search in Google Scholar

[26] KARAPINAR, E.: A short survey on the recent fixed point results on b-metric spaces, Constr. Math. Anal. 1 (2018), no. 1, 15–44. https://dx.doi.org/10.33205/cma.45303410.33205/cma.453034 Search in Google Scholar

[27] KHEMARATCHATAKUMTHORN, T.—PONGSRIIAM, P.: Remarks on b-metric and metric-preserving functions, Math. Slovaca 68 (2018), no. 5, 1009–1016. https://doi.org/10.1515/ms-2017-016310.1515/ms-2017-0163 Search in Google Scholar

[28] KHEMARATCHATAKUMTHORN, T.—PONGSRIIAM, P.—SAMPHAVAT, S.: Further remarks on b-metrics, metric-preserving functions, and other related metrics, Int. J. Math. Comput. Sci. 14 (2019), no. 2, 473–480. http://ijmcs.future-in-tech.net/14.2/R-Pongsriiam2.pdf Search in Google Scholar

[29] KHEMARATCHATAKUMTHORN, T.—TERMWUTTIPONG, I.: Metric-preserving functions, w-distances and Cauchy w-distances, Thai J. Math. 5 (2012), 51–56. http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/20 Search in Google Scholar

[30] KIRK, W. A.—SHAHZAD, N.: Fixed Point Theory in Distance Spaces. Springer, Cham, 2014. https://link.springer.com/book/10.1007/978-3-319-10927-510.1007/978-3-319-10927-5 Search in Google Scholar

[31] MARTÍN, J.—MAYOR, G.—VALERO, O.: A fixed point theorem for asymmetric distances via aggregation functions, In: Proceedings of the 6th International Summer School on Aggregation Operators, 2011, pp. 217–222. https://www.researchgate.net/profile/O_Valero/publication/261834817_A__point_theorem_for_asymmetric_distances_via_aggregation_functions/_fixed_links/0c960535e118e9a63e000000/A-fixed-point-theorem-for-asymmetric-distances-via-aggregation-functions.pdf Search in Google Scholar

[32] MASSANET, S.—VALERO, O.: New results on metric aggregation, In: Proceedings of the 17th Spanish Conference on Fuzzy Technology and Fuzzy Logic, Estylf, 2012, pp. 558–563. http://estylf2012.eii.uva.es/ActasESTYLF2012.pdf Search in Google Scholar

[33] MAYOR, G.—VALERO, O.: Aggregation of asymmetric distances in computer science, Inform. Sciences 180 (2010), 803–812. https://doi.org/10.1016/j.ins.2009.06.02010.1016/j.ins.2009.06.020 Search in Google Scholar

[34] MAYOR, G.—VALERO, O.: Metric aggregation functions revisited, European J. Combin. 80 (2019), 390–400. https://doi.org/10.1016/j.ejc.2018.02.03710.1016/j.ejc.2018.02.037 Search in Google Scholar

[35] OLSON, D. L.: Comparison of weights in TOPSIS models, Math. Comput. Modelling, 40 (2004), no. 7–8, 721–727. https://doi.org/10.1016/j.mcm.2004.10.00310.1016/j.mcm.2004.10.003 Search in Google Scholar

[36] OPRICOVIC, S.—TZENG, G. H.: Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European J. Oper. Res. 156 (2004), no. 2, 445–455. https://doi.org/10.1016/S0377-2217(03)00020-110.1016/S0377-2217(03)00020-1 Search in Google Scholar

[37] POKORNÝ, I.: Some remarks on metric-preserving functions, Tatra Mt. Math. Publ. 2 (1993), 65–68. https://www.sav.sk/journals/uploads/1203090709pokorn.pdf Search in Google Scholar

[38] POKORNÝ, I.: Some remarks on metric preserving functions of several variables, Tatra Mt. Math. Publ. 8 (1996), 89–92. Search in Google Scholar

[39] POKORNÝ, I.: Remarks on the sum of metrics, Tatra Mt. Math. Publ. 14 (1998), 63–65. Search in Google Scholar

[40] PONGSRIIAM, P.—TERMWUTTIPONG, I.: On metric-preserving functions and fixed point theorems, Fixed Point Theory Appl. 2014 Article ID 2014:179 (2014), 14 pp. https://doi.org/10.1186/1687-1812-2014-17910.1186/1687-1812-2014-179 Search in Google Scholar

[41] PONGSRIIAM, P.—TERMWUTTIPONG, I.: Remarks on ultrametrics and metric-preserving functions, Abstr. Appl. Anal. 2014 Article ID 163258 (2014), 9 pp. https://doi.org/10.1155/2014/16325810.1155/2014/163258 Search in Google Scholar

[42] SAMPHAVAT, S.—KHEMARATCHATAKUMTHORN, T.—PONGSRIIAM, P.: Remarks on b-metrics, ultrametrics, and metric-preserving functions, Math. Slovaca 70 (2020), no. 1, 61–70. https://doi.org/10.1515/ms-2017-033110.1515/ms-2017-0331 Search in Google Scholar

[43] SREENIVASAN, T. K.: Some properties of distance functions, J. Indian Math. Soc. (N.S.) 11 (1947), 38–43. http://www.informaticsjournals.com/index.php/jims/article/view/17103 Search in Google Scholar

[44] TERMWUTTIPONG, I.—OUDKAM, P.: Total boundedness, completeness and uniform limits of metric-preserving functions, Ital. J. Pure Appl. Math. 18 (2005), 187–196. Search in Google Scholar

[45] TERPE, F.: Metric preserving functions of several variables, In: Proc. Conf. Topology and Measure V, (Binz, 1987), Wissensch. Beitr., Ernst-Moritz-Arndt Univ., Greifswald, 1988, pp. 169—174. Search in Google Scholar

[46] TUROBOŚ, F.: On characterization of functions preserving metric-type conditions via triangular and polygonal structures, arXiv:2011.14110 [math.MG] (2020), 1–18. https://arxiv.org/abs/2011.14110 Search in Google Scholar

[47] VALLIN, R. W.: On metric preserving functions and infinite derivatives, Acta Math. Univ. Comenian. (N.S.) 67 (1998), no. 2, 373–376. http://emis.impa.br/EMIS/journals/AMUC/_vol-67/_no_2/_vallin/vallin.pdf Search in Google Scholar

[48] VALLIN, R. W.: Continuity and differentiability aspects of metric preserving functions, Real Anal. Exchange 25 (2000), no. 2, 849–868. https://projecteuclid.org/download/pdf_1/euclid.rae/123099541910.2307/44154040 Search in Google Scholar

[49] VALLIN, R. W.—DOVGOSHEY, O. A.: P-adic metric preserving functions and their analogues, Math. Slovaca 71 (2021), no. 2, 391–408. https://arxiv.org/abs/1912.1041110.1515/ms-2017-0476 Search in Google Scholar

[50] VAN AN, T.—VAN DUNG, N.—KADELBURG, Z.—RADENOVIĆ, S.: Various generalizations of metric spaces and fixed point theorems, RACSAM Rev. R. Acad. Cienc. Exactas Fìs. Nat. Ser. A Mat. 109 (2014), no. 1. 175—198. https://doi.org/10.1007/s13398-014-0173-710.1007/s13398-014-0173-7 Search in Google Scholar

[51] WILSON, W. A.: On certain types of continuous transformations of metric spaces, Amer. J. Math. 57 (1935), 62–68. https://doi.org/10.2307/237201910.2307/2372019 Search in Google Scholar