Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings

Meryem Şenocak; Erdal Güner

doi:10.31801/cfsuasmas.1038245

Research Article

Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings

Year 2023, Volume: 72 Issue: 1, 71 - 83, 30.03.2023

Meryem Şenocak Erdal Güner

https://doi.org/10.31801/cfsuasmas.1038245

Abstract

In this article we would like to present a new type of fuzzy contractive mappings which are called $\alpha-\phi-\mathcal{M}^{0}$ fuzzy contractive and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive, and then we demonstrate two theorems which ensure the existence of a fixed point for these two types of mappings. And so we combine and generalize some existing notions in the literature ([5], [7]). Proved these theorems in the extended fuzzy metric spaces are in the more general version than the existing in the literature ones.

Keywords

Fixed-point, extended fuzzy metric space, fuzzy contractive mapping

References

Banach, S., Sur les oprations dans les ensembles abstrails et leur application aux quations intgrales, Fund Math., 3 (1922), 133-181.
Chang, C., L., Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24 (1968), 182-190. https://doi.org/10.1016/0022-247X(68)90057-7
Di Bari, C., Vetro, C., Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13(4) (2005), 973-982.
George, A., Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399. http://dx.doi.org/10.1016/0165-0114(94)90162-7
Gopal, D., Vetro, C., Some new fixed point theorems in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 11(3) (2014), 95-107.
Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
Gregori, V., Minana, J. J., Miravet, D., Extended fuzzy metrics and fixed point theorems, Mathematics Journal, 7 (2019), 303. https://doi.org/10.3390/math7030303
Gregori, V., Romaguera, S., Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2014), 411-420. DOI:10.1016/S0165-0114(03)00161-1
Gregori, V., Sapena, A., On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
Gregori, V., Minana, J. J. Morillas, S., A note on convergence in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 11 (2014), 75-85. DOI:10.22111/IJFS.2014.1625
Huang, H., Caric, B., Dosenovic, T., Rakic, D., Brdar, M., Fixed point theorems in fuzzy metric spaces via fuzzy F-contraction, Mathematics Journal, 9 (2021), 641. https://doi.org/10.3390/math9060641
Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), 1-9. DOI: https://doi.org/10.1017/S0004972700001659
Kramosil, I., Michalek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
Mihet, D., Fuzzy ψ− contractive mappings in non-Archimedean fuzzy metric space, Fuzzy Sets and Systems, 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006
Mihet, D., A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Set. Syst., 251 (2014), 83-91.16
Park, J. S., Kim, S. Y., A fixed point theorem in a fuzzy metric space, F. J. M. S., 1(6) (1999), 927-934.
Samet, B. Vetro, C. Vetro, P., Fixed point theorems for α − ψ contractive type mappings, Nonlinear Analysis Theory Methods and Applications, 75 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014
Schwizer, B., Sklar, A., Statistical metric spaces, Pacific Journal of Mathematics 10 (1960), 315-367.
Shen, Y., Qiu, D., Chen, W., Fixed point theorems in fuzzy metric spaces, App. Mathematics Letters, 25 (2012), 138-141. https://doi.org/10.1016/j.aml.2011.08.002
Zadeh, L.A., Fuzzy sets, Inform. Control, 8 (1965), 338-353.

Year 2023, Volume: 72 Issue: 1, 71 - 83, 30.03.2023

Meryem Şenocak Erdal Güner

https://doi.org/10.31801/cfsuasmas.1038245

Abstract

References

Banach, S., Sur les oprations dans les ensembles abstrails et leur application aux quations intgrales, Fund Math., 3 (1922), 133-181.
Chang, C., L., Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24 (1968), 182-190. https://doi.org/10.1016/0022-247X(68)90057-7
Di Bari, C., Vetro, C., Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13(4) (2005), 973-982.
George, A., Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399. http://dx.doi.org/10.1016/0165-0114(94)90162-7
Gopal, D., Vetro, C., Some new fixed point theorems in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 11(3) (2014), 95-107.
Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
Gregori, V., Minana, J. J., Miravet, D., Extended fuzzy metrics and fixed point theorems, Mathematics Journal, 7 (2019), 303. https://doi.org/10.3390/math7030303
Gregori, V., Romaguera, S., Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2014), 411-420. DOI:10.1016/S0165-0114(03)00161-1
Gregori, V., Sapena, A., On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
Gregori, V., Minana, J. J. Morillas, S., A note on convergence in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 11 (2014), 75-85. DOI:10.22111/IJFS.2014.1625
Huang, H., Caric, B., Dosenovic, T., Rakic, D., Brdar, M., Fixed point theorems in fuzzy metric spaces via fuzzy F-contraction, Mathematics Journal, 9 (2021), 641. https://doi.org/10.3390/math9060641
Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), 1-9. DOI: https://doi.org/10.1017/S0004972700001659
Kramosil, I., Michalek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
Mihet, D., Fuzzy ψ− contractive mappings in non-Archimedean fuzzy metric space, Fuzzy Sets and Systems, 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006
Mihet, D., A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Set. Syst., 251 (2014), 83-91.16
Park, J. S., Kim, S. Y., A fixed point theorem in a fuzzy metric space, F. J. M. S., 1(6) (1999), 927-934.
Samet, B. Vetro, C. Vetro, P., Fixed point theorems for α − ψ contractive type mappings, Nonlinear Analysis Theory Methods and Applications, 75 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014
Schwizer, B., Sklar, A., Statistical metric spaces, Pacific Journal of Mathematics 10 (1960), 315-367.
Shen, Y., Qiu, D., Chen, W., Fixed point theorems in fuzzy metric spaces, App. Mathematics Letters, 25 (2012), 138-141. https://doi.org/10.1016/j.aml.2011.08.002
Zadeh, L.A., Fuzzy sets, Inform. Control, 8 (1965), 338-353.

There are 20 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Meryem Şenocak 0000-0002-2988-9419 Erdal Güner 0000-0003-4749-1321
Publication Date	March 30, 2023
Submission Date	December 18, 2021
Acceptance Date	August 31, 2022
Published in Issue	Year 2023 Volume: 72 Issue: 1

Cite

APA	Şenocak, M., & Güner, E. (2023). Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 71-83. https://doi.org/10.31801/cfsuasmas.1038245
AMA	Şenocak M, Güner E. Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2023;72(1):71-83. doi:10.31801/cfsuasmas.1038245
Chicago	Şenocak, Meryem, and Erdal Güner. “Fixed-Point Theorems in Extended Fuzzy Metric Spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ Fuzzy Contractive Mappings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 1 (March 2023): 71-83. https://doi.org/10.31801/cfsuasmas.1038245.
EndNote	Şenocak M, Güner E (March 1, 2023) Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 71–83.
IEEE	M. Şenocak and E. Güner, “Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 1, pp. 71–83, 2023, doi: 10.31801/cfsuasmas.1038245.
ISNAD	Şenocak, Meryem - Güner, Erdal. “Fixed-Point Theorems in Extended Fuzzy Metric Spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ Fuzzy Contractive Mappings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (March 2023), 71-83. https://doi.org/10.31801/cfsuasmas.1038245.
JAMA	Şenocak M, Güner E. Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:71–83.
MLA	Şenocak, Meryem and Erdal Güner. “Fixed-Point Theorems in Extended Fuzzy Metric Spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ Fuzzy Contractive Mappings”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 1, 2023, pp. 71-83, doi:10.31801/cfsuasmas.1038245.
Vancouver	Şenocak M, Güner E. Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):71-83.