Some Fixed Point Theorems in Extended Fuzzy Metric Spaces

Yıl 2023, , 67 - 75, 31.03.2023

Meryem Şenocak , Erdal Güner

https://doi.org/10.18185/erzifbed.1146294

Öz

In this article, we would like to present a newly fuzzy contraction mapping and using it we would like to prove a fixed point theorem. In fact, we transfer this contraction mapping, first defined in metric spaces [15], and then transferred to fuzzy metric spaces [9] with modification, to extended fuzzy metric spaces [6]. And so we prove some fixed point theorems [9] existing in the literature in the new spaces [6].

Anahtar Kelimeler

Fixed-point, Extended fuzzy metric space, Fuzzy contraction.

Kaynakça

• Banach, S., 1922. Sur les oprations dans les ensembles abstrails et leur application aux quations intgrales, Fund Math., vol. 3, 133-181.
• Di Bari, C., Vetro, C., 2005. Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13(4), 973-982.
• George, A., Veeramani, P., 1994. On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64, 395-399.
• Gopal, D. and Vetro, C., 2014. Some new fixed point theorems in fuzzy metric spaces, Iranian Journal of Fuzzy Systems,Vol.11, No.3, 95-107.
• Grabiec, M., 1988. Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27, 385-389.
• Gregori, V., Minana, J. J. and Miravet, D., 2019. Extended fuzzy metrics and fixed point theorems, Mathematics Journal, 7, 303.
• Gregori, V., Romaguera, S., 2014. Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, 144, 411-420.
• Gregori,V., Sapena, A., 2002. On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125, 245-252.
• Huang, H., Caric, B., Dosenovic, T., Rakic, D. and Brdar, M., 2021.Fixed point theorems in fuzzy metric spaces via fuzzy F-contraction, Mathematics Journal, 9, 641.10
• Kramosil, I., Michalek, J., 1975. Fuzzy metrics and statistical metric spaces, Kybernetika, 11, 336-344.
• Mihet, D., 2008. Fuzzy ψ- contractive mappings in non-Archimedean fuzzy metric space, Fuzzy Sets and Systems, 159, 739-744. 10.
• Mihet, D., 2014. A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Set. Syst., 251, 83-91,16.
• Samet, B. Vetro, C. Vetro, P., 2012. Fixed point theorems for α-ψ contractive type mappings, Nonlinear Analysis Theory, Methods and Applications, 75, 2154-2165.
• Schwizer, B., Sklar, A., 1960. Statistical metric spaces, Pacific Journal of Mathematics 10, 315-367.
• Wardowski, D., 2012. Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012, 94.
• Zadeh, L.A., 1965. Fuzzy sets, Inform. Control, 8, 338-353.