Research Article
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Year 2022, Volume: 5 Issue: 3, 347 - 359, 30.09.2022
https://doi.org/10.53006/rna.1140743

Abstract

References

  • [1] M. Abbas, B. Ali, S. Romaguera, Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness, Filomat 29 (2015) 1217-1222.
  • [2] C. Alegre, H. D˘ ag, S. Romaguera, P. Tirado, Characterizations of quasi-metric completeness in terms of Kannan-type fixed point theo- rems, Hacettepe J. Math. Stat. 46 (2017) 67-76.
  • [3] F. Castro-Company, S. Romaguera, P. Tirado, The bicompletion of fuzzy quasi-metric spaces, Fuzzy Sets Syst. 166 (2011) 56-64.
  • [4] S.K. Chatterjea, Fixed point theorems. C. R. Acad. Bulgare Sci. 25 (1972) 727-730.
  • [5] Y.J. Cho, M. Grabiec, V. Radu, On non Symmetric Topological and Probabilistic Structures, Nova Science Publisher, Inc. New York, 2006
  • [6] S. Cobza¸ s, Functional Analysis in Asymmetric Normed spaces, Frontiers in Mathematics, Birkha˘ user/Springer Basel AG, Basel, Switzer- land, 2013.
  • [7] P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, New York, 1982.
  • [8] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395-399.
  • [9] A. George, P. Veeramani, On some results of analysis of fuzzy metric spaces, Fuzzy Sets Syst. 90 (1997) 365-368.
  • [10] V. Gregori, S. Romaguera, Fuzzy quasi-metric spaces, Appl. Gen. Topol. 5 (2004) 129-136.
  • [11] T.K. Hu, On a fixed point theorem for metric spaces, Amer. Math. Monthly 74 (1967) 436-437.
  • [12] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968) 71-76.
  • [13] A.W. Kirk, Caristi’s fixed point theorem and metric convexity, Colloq. Math. 36 (1976) 81-86.
  • [14] E. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic, Dordrecht, 2000.
  • [15] I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975) 326-334.
  • [16] R.P. Pant, A. Pant, R.M. Nikolic, S.N. Jesic, A characterization of completeness of Menger PM-spaces, J. Fixed Point Theory Appl. (2019) 21:90.
  • [17] V. Radu, Some suitable metrics on fuzzy metric spaces, Fixed Point Theory 5 (2004) 323-347.
  • [18] S. Romaguera, A fixed point theorem of Kannan type that characterizes fuzzy metric completeness, Filomat 34 (2020) 4811-4819.
  • [19] S. Romaguera, w-distances on fuzzy metic spaces and fixed points, Mathematics 2020, 8, 1909.
  • [20] S. Romaguera, P. Tirado, A characterization of quasi-metric completeness in terms of α − ψ-contractive mappings having fixed points, Mathematics 2020, 8, 16.
  • [21] S. Romaguera, P. Tirado, Characterizing complete fuzzy metric spaces via fixed point results, Mathematics 2020, 8, 273.
  • [22] S. Romaguera, P. Tirado, Contractive self maps of α − ψ-type on fuzzy metric spaces, Dyn. Syst. Appl. 30 (2021) 359-370.
  • [23] P.V. Subrahmanyam, Completeness and fixed-points, Mh. Math. 80 (1975) 325-330.
  • [24] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861- 1869.
  • [25] T. Suzuki, W. Takahashi, Fixed point theorems and characterizations of metric completeness, Top. Methods Nonlinear Anal. 8 (1996) 371-382.

Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces

Year 2022, Volume: 5 Issue: 3, 347 - 359, 30.09.2022
https://doi.org/10.53006/rna.1140743

Abstract

We characterize the completeness of fuzzy quasi-metric spaces by means of a fixed point theorem of Kannan-type.
Thus, we extend the classical characterization of metric completeness due to Subrahmanyam as well as recent results
in the literature on the characterization of quasi-metric completeness and fuzzy metric completeness, respectively. We
also introduce and discuss contractions of Chatterjea-type in this asymmetric context.

References

  • [1] M. Abbas, B. Ali, S. Romaguera, Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness, Filomat 29 (2015) 1217-1222.
  • [2] C. Alegre, H. D˘ ag, S. Romaguera, P. Tirado, Characterizations of quasi-metric completeness in terms of Kannan-type fixed point theo- rems, Hacettepe J. Math. Stat. 46 (2017) 67-76.
  • [3] F. Castro-Company, S. Romaguera, P. Tirado, The bicompletion of fuzzy quasi-metric spaces, Fuzzy Sets Syst. 166 (2011) 56-64.
  • [4] S.K. Chatterjea, Fixed point theorems. C. R. Acad. Bulgare Sci. 25 (1972) 727-730.
  • [5] Y.J. Cho, M. Grabiec, V. Radu, On non Symmetric Topological and Probabilistic Structures, Nova Science Publisher, Inc. New York, 2006
  • [6] S. Cobza¸ s, Functional Analysis in Asymmetric Normed spaces, Frontiers in Mathematics, Birkha˘ user/Springer Basel AG, Basel, Switzer- land, 2013.
  • [7] P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, New York, 1982.
  • [8] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395-399.
  • [9] A. George, P. Veeramani, On some results of analysis of fuzzy metric spaces, Fuzzy Sets Syst. 90 (1997) 365-368.
  • [10] V. Gregori, S. Romaguera, Fuzzy quasi-metric spaces, Appl. Gen. Topol. 5 (2004) 129-136.
  • [11] T.K. Hu, On a fixed point theorem for metric spaces, Amer. Math. Monthly 74 (1967) 436-437.
  • [12] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968) 71-76.
  • [13] A.W. Kirk, Caristi’s fixed point theorem and metric convexity, Colloq. Math. 36 (1976) 81-86.
  • [14] E. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic, Dordrecht, 2000.
  • [15] I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975) 326-334.
  • [16] R.P. Pant, A. Pant, R.M. Nikolic, S.N. Jesic, A characterization of completeness of Menger PM-spaces, J. Fixed Point Theory Appl. (2019) 21:90.
  • [17] V. Radu, Some suitable metrics on fuzzy metric spaces, Fixed Point Theory 5 (2004) 323-347.
  • [18] S. Romaguera, A fixed point theorem of Kannan type that characterizes fuzzy metric completeness, Filomat 34 (2020) 4811-4819.
  • [19] S. Romaguera, w-distances on fuzzy metic spaces and fixed points, Mathematics 2020, 8, 1909.
  • [20] S. Romaguera, P. Tirado, A characterization of quasi-metric completeness in terms of α − ψ-contractive mappings having fixed points, Mathematics 2020, 8, 16.
  • [21] S. Romaguera, P. Tirado, Characterizing complete fuzzy metric spaces via fixed point results, Mathematics 2020, 8, 273.
  • [22] S. Romaguera, P. Tirado, Contractive self maps of α − ψ-type on fuzzy metric spaces, Dyn. Syst. Appl. 30 (2021) 359-370.
  • [23] P.V. Subrahmanyam, Completeness and fixed-points, Mh. Math. 80 (1975) 325-330.
  • [24] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861- 1869.
  • [25] T. Suzuki, W. Takahashi, Fixed point theorems and characterizations of metric completeness, Top. Methods Nonlinear Anal. 8 (1996) 371-382.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Salvador Romaguera Bonilla

Publication Date September 30, 2022
Published in Issue Year 2022 Volume: 5 Issue: 3

Cite

APA Romaguera Bonilla, S. (2022). Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces. Results in Nonlinear Analysis, 5(3), 347-359. https://doi.org/10.53006/rna.1140743
AMA Romaguera Bonilla S. Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces. RNA. September 2022;5(3):347-359. doi:10.53006/rna.1140743
Chicago Romaguera Bonilla, Salvador. “Contractions of Kannan-Type and of Chatterjea-Type on Fuzzy Quasi-Metric Spaces”. Results in Nonlinear Analysis 5, no. 3 (September 2022): 347-59. https://doi.org/10.53006/rna.1140743.
EndNote Romaguera Bonilla S (September 1, 2022) Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces. Results in Nonlinear Analysis 5 3 347–359.
IEEE S. Romaguera Bonilla, “Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces”, RNA, vol. 5, no. 3, pp. 347–359, 2022, doi: 10.53006/rna.1140743.
ISNAD Romaguera Bonilla, Salvador. “Contractions of Kannan-Type and of Chatterjea-Type on Fuzzy Quasi-Metric Spaces”. Results in Nonlinear Analysis 5/3 (September 2022), 347-359. https://doi.org/10.53006/rna.1140743.
JAMA Romaguera Bonilla S. Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces. RNA. 2022;5:347–359.
MLA Romaguera Bonilla, Salvador. “Contractions of Kannan-Type and of Chatterjea-Type on Fuzzy Quasi-Metric Spaces”. Results in Nonlinear Analysis, vol. 5, no. 3, 2022, pp. 347-59, doi:10.53006/rna.1140743.
Vancouver Romaguera Bonilla S. Contractions of Kannan-type and of Chatterjea-type on fuzzy quasi-metric spaces. RNA. 2022;5(3):347-59.