Some new classes of fuzzy contraction defined by means of fuzzy negations and related fixed point theorems

Martínez-Moreno J., Gopal D., Aldemir B., AYGÜN H., Valero O.

International Journal of General Systems, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1080/03081079.2026.2620537
  • Dergi Adı: International Journal of General Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: archimedean t-norm, fixed points, fuzzy contractive mappings, Fuzzy metric spaces, strict negation function, strong negation function
  • Kocaeli Üniversitesi Adresli: Evet

Özet

Using the notion of fuzzy negation functions which naturally arises in the theory and applications of fuzzy logic, we enlarge the class of fuzzy ψ-contractions of (Formula presented.) type as well as the class of fuzzy (Formula presented.) contractions and generalize corresponding fixed point theorems. We show that strict negations, strong negations and Archimedean t-norms play a central role in the aforesaid fixed point theorems. Appropriate examples that illustrate the exposed theory are provided. In the process, we obtain a new type of topology (as well as convergence and completeness) for the fuzzy metric spaces that suggesting a potential new research avenue to explore the subject.