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September 10, 2025International journal of mathematics and computer science0 citations

Fixed Point Theorems in Fuzzy Metric Spaces via Generalized Rational-Type Contractions.

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KDKrishnamoorthy DineshDr. Bhim Rao Ambedkar UniversityDGDritan GerbetiUniversity of Shkodra "Luigj Gurakuqi"KZKastriot ZotoEqrem Çabej University

Key Points

  • New fixed point theorems establish conditions for unique fixed points in fuzzy metric spaces.
  • The findings include incorporating nonlinear contractive conditions and fuzzy distances to prove convergence.
  • Utilizing properties of fuzzy metrics and continuous t-norms, sufficient conditions for mapping are derived.
  • An illustrative example demonstrates the main results and applicability of the proposed theorems.

Abstract

In this paper, we create new fixed point (FP) theorems for self-mappings in fuzzy metric spaces (FMS). Utilizing properties of fuzzy metrics (FM) and continuous t-norms, we derive sufficient conditions under which a mapping admits a unique FP, and we prove that the sequence of iterates converges to this point. The results presented extend and generalize existing theorems by incorporating nonlinear contractive conditions involving fuzzy distances. An example is provided to illustrate the applicability of the main results. A graphical representation of the FM is also discussed.

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Cite This Study

Dinesh et al. (2025) studied this question.

synapsesocial.com/papers/68c1d7f654b1d3bfb60fa37fhttps://doi.org/10.69793/ijmcs/04.2025/zoto
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