Year 2022,
Volume: 5 Issue: 3, 347 - 359, 30.09.2022
Salvador Romaguera Bonilla
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
Salvador Romaguera Bonilla
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.