FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS
Yıl 2025,
Cilt: 8 Sayı: 1, 33 - 39, 31.01.2025
Meryem Şenocak
Öz
In this article, an interpolative contraction existing in the literature is adapted to different fuzzy metric spaces. Using this contraction, a fixed point theorem in two fuzzy metric spaces is proven and an example is presented. Thus, a more general form of some concepts and theorems existing in the literature has been obtained.
Etik Beyan
I declare that this study is an original study, that I have acted in accordance with scientific ethical principles and rules at all stages, and that I have cited the sources for the data and information.
Destekleyen Kurum
There is no support from any institution.
Teşekkür
I would like to thank the editors who will review this work for their contributions.
Kaynakça
- S. Banach, Sur les oprations dans les ensembles abstrails et leur application aux quations intgrales, Fund Math., Vol.3, pp.133-181 (1922).
- A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems., Vol.64, pp.395-399 (1994). Doi:10.1016/0165-0114(94)90162-7.
- M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems., Vol.27, pp.385-389 (1988). Doi:10.1016/0165-0114(88)90064-4.
- V. Gregori, J. J. Minana, D. Miravet, Extended fuzzy metrics and _xed point theorems, Mathematics Journal, Vol.7, pp.303 (2019). Doi:10.3390/math7030303.
- V. Gregori, S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Sets and Systems, Vol.144, pp.411-420 (2014). Doi:10.1016/S0165-0114(03)00161-1.
- V. Gregori, A. Sapena, On _xed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, Vol.125, pp.245-252 (2002). Doi:10.1016/S0165-0114(00)00088-9.
- V. Istratescu, An introduction to theory of probabilistic metric spaces with applications, Ed. Tehnica, Bucure_sti-Romanian, (1974).
- E. Karapinar, R. P. Agarwal, H. Aydi, Interpolative Reich-Rus-Ciric type contractions on partial metric spaces, Mathematics, Vol.6, pp.256 (2018).
- I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, Vol.11, pp.336-344 (1975).
- D. Mihet, Fuzzy contractive mappings in non-Archimedean fuzzy metric space, Fuzzy Sets and Systems, Vol.159, pp.736-744 (2008). Doi:10.1016/j.fss.2007.07.006.
- B. Schwizer, A. Sklar, Statistical metric spaces, Paci_c Journal of Mathematics, Vol.10, pp.315-367 (1960).
- L. A. Zadeh, Fuzzy sets, Inform. Control., Vol.8, pp.338-353 (1965).