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

J. Martínez-Moreno et al.

International Journal of General Systems2026https://doi.org/10.1080/03081079.2026.2620537article
AJG 1ABDC A
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0.50

Abstract

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.

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https://doi.org/https://doi.org/10.1080/03081079.2026.2620537

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@article{j.2026,
  title        = {{Some new classes of fuzzy contraction defined by means of fuzzy negations and related fixed point theorems}},
  author       = {J. Martínez-Moreno et al.},
  journal      = {International Journal of General Systems},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1080/03081079.2026.2620537},
}

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