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

Yıl: 2023 Cilt: 72 Sayı: 1 Sayfa Aralığı: 71 - 83 Metin Dili: İngilizce İndeks Tarihi: 25-05-2023

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

Öz:
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.
Anahtar Kelime: Fixed-point extended fuzzy metric space fuzzy contractive mapping

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
• [1] Banach, S., Sur les oprations dans les ensembles abstrails et leur application aux quations intgrales, Fund Math., 3 (1922), 133-181.
• [2] 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
• [3] 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.
• [4] 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
• [5] Gopal, D., Vetro, C., Some new fixed point theorems in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 11(3) (2014), 95-107.
• [6] 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
• [7] 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
• [8] 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
• [9] 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
• [10] 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
• [11] 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
• [12] Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering dis- tances between the points, Bull. Aust. Math. Soc. 30 (1984), 1-9. DOI: https://doi.org/10.1017/S0004972700001659
• [13] Kramosil, I., Michalek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), 336-344.
• [14] 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
• [15] Mihet, D., A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Set. Syst., 251 (2014), 83-91.16
• [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.
• [17] 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
• [18] Schwizer, B., Sklar, A., Statistical metric spaces, Pacific Journal of Mathematics 10 (1960), 315-367.
• [19] 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
• [20] Zadeh, L.A., Fuzzy sets, Inform. Control, 8 (1965), 338-353.
 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. , 71 - 83. 10.31801/cfsuasmas.1038245 Chicago 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. (2023): 71 - 83. 10.31801/cfsuasmas.1038245 MLA 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. , 2023, ss.71 - 83. 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. . 2023; 71 - 83. 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. . 2023; 71 - 83. 10.31801/cfsuasmas.1038245 IEEE 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." , ss.71 - 83, 2023. 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". (2023), 71-83. https://doi.org/10.31801/cfsuasmas.1038245
 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. 10.31801/cfsuasmas.1038245 Chicago 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, no.1 (2023): 71 - 83. 10.31801/cfsuasmas.1038245 MLA 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, vol.72, no.1, 2023, ss.71 - 83. 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. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(1): 71 - 83. 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. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(1): 71 - 83. 10.31801/cfsuasmas.1038245 IEEE 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." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72, ss.71 - 83, 2023. 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 (2023), 71-83. https://doi.org/10.31801/cfsuasmas.1038245