Research Article
BibTex RIS Cite

FIXED POINT THEOREMS IN SOME FUZZY METRIC SPACES VIA INTERPOLATIVE CONTRACTIONS

Year 2025, , 33 - 39, 31.01.2025
https://doi.org/10.33773/jum.1446824

Abstract

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.

Ethical Statement

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.

Supporting Institution

There is no support from any institution.

Thanks

I would like to thank the editors who will review this work for their contributions.

References

  • 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).
Year 2025, , 33 - 39, 31.01.2025
https://doi.org/10.33773/jum.1446824

Abstract

References

  • 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).
There are 12 citations in total.

Details

Primary Language English
Subjects Topology
Journal Section Research Article
Authors

Meryem Şenocak 0000-0002-2988-9419

Publication Date January 31, 2025
Submission Date July 30, 2024
Acceptance Date December 2, 2024
Published in Issue Year 2025

Cite

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. January 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, no. 1 (January 2025): 33-39. https://doi.org/10.33773/jum.1446824.
EndNote Şenocak M (January 1, 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, vol. 8, no. 1, pp. 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 (January 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, vol. 8, no. 1, 2025, pp. 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.