On the fixed points of Kannan contraction mappings on fuzzy metric spaces

Articles in Press

Document Type : Research Paper

Authors
Morteza Saheli
Seyed Ali Mohammad Mohsenialhosseini
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
10.22075/ijnaa.2026.41061.5678
Abstract
In this paper, comparison functions are employed to introduce and investigate new classes of contractive mappings in fuzzy and classical metric spaces. After defining $\varphi$-large contractions and establishing fixed-point results for them in fuzzy and classical settings, the study focuses on generalizations of Khan-type contractions. In this regard, $\varphi$-large Khan contractions are first introduced in fuzzy metric spaces, and the existence of fixed points is proved for such mappings. Their counterparts in classical metric spaces are then defined, and by using the results obtained in fuzzy metric spaces, the existence of fixed points in the classical case is also established. Furthermore, large Khan contractions and extended $\varphi$-large Khan contractions are studied as generalizations of the aforementioned mappings, and sufficient conditions ensuring the existence of fixed points in both fuzzy and classical metric spaces are provided. Finally, a more general form of large Khan contractions is introduced in fuzzy metric spaces, and the existence of fixed points for functions in this broader class is proved. The results of this study not only expand the theory of fixed points in fuzzy metric spaces, but also provide a more general framework for analyzing stability and convergence in related problems.
Keywords
Large contraction
Kannan contraction
Fuzzy metric space
Fixed point
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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 29 October 2026

  • Receive Date 02 May 2026
  • Revise Date 16 June 2026
  • Accept Date 21 June 2026