Araştırma Makalesi
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FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS

Yıl 2025, Cilt: 8 Sayı: 1, 33 - 39, 31.01.2025
https://doi.org/10.33773/jum.1446824

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).
Yıl 2025, Cilt: 8 Sayı: 1, 33 - 39, 31.01.2025
https://doi.org/10.33773/jum.1446824

Öz

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).
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Topoloji
Bölüm Araştırma Makalesi
Yazarlar

Meryem Şenocak 0000-0002-2988-9419

Yayımlanma Tarihi 31 Ocak 2025
Gönderilme Tarihi 30 Temmuz 2024
Kabul Tarihi 2 Aralık 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 1

Kaynak Göster

APA Şenocak, M. (2025). FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS. Journal of Universal Mathematics, 8(1), 33-39. https://doi.org/10.33773/jum.1446824
AMA Şenocak M. FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS. JUM. Ocak 2025;8(1):33-39. doi:10.33773/jum.1446824
Chicago Şenocak, Meryem. “FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS”. Journal of Universal Mathematics 8, sy. 1 (Ocak 2025): 33-39. https://doi.org/10.33773/jum.1446824.
EndNote Şenocak M (01 Ocak 2025) FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS. Journal of Universal Mathematics 8 1 33–39.
IEEE M. Şenocak, “FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS”, JUM, c. 8, sy. 1, ss. 33–39, 2025, doi: 10.33773/jum.1446824.
ISNAD Şenocak, Meryem. “FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS”. Journal of Universal Mathematics 8/1 (Ocak 2025), 33-39. https://doi.org/10.33773/jum.1446824.
JAMA Şenocak M. FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS. JUM. 2025;8:33–39.
MLA Şenocak, Meryem. “FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS”. Journal of Universal Mathematics, c. 8, sy. 1, 2025, ss. 33-39, doi:10.33773/jum.1446824.
Vancouver Şenocak M. FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS. JUM. 2025;8(1):33-9.