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Fixed-Point Theorems for Fuzzy Mappings

Author

Listed:
  • Allan Edley Ramos de Andrade

    (Federal University of Mato Grosso do Sul, CPTL, Três Lagoas 79613-000, Brazil)

  • Vinícius Francisco Wasques

    (Ilum School of Science, CNPEM, Campinas 13087-548, Brazil)

Abstract

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra.

Suggested Citation

  • Allan Edley Ramos de Andrade & Vinícius Francisco Wasques, 2024. "Fixed-Point Theorems for Fuzzy Mappings," Mathematics, MDPI, vol. 12(14), pages 1-8, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2165-:d:1432556
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    References listed on IDEAS

    as
    1. Samina Batul & Dur-e-Shehwar Sagheer & Muhammad Anwar & Hassen Aydi & Vahid Parvaneh & Ivan Giorgio, 2022. "Fuzzy Fixed Point Results of Fuzzy Mappings on b-Metric Spaces via α∗,F-Contractions," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-8, July.
    2. Dur-e-Shehwar Sagheer & Zainab Rahman & Samina Batul & Ahmad Aloqaily & Nabil Mlaiki, 2023. "Existence of Fuzzy Fixed Points and Common Fuzzy Fixed Points for FG -Contractions with Applications," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
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    1. Dur-e-Shehwar Sagheer & Zainab Rahman & Samina Batul & Ahmad Aloqaily & Nabil Mlaiki, 2023. "Existence of Fuzzy Fixed Points and Common Fuzzy Fixed Points for FG -Contractions with Applications," Mathematics, MDPI, vol. 11(18), pages 1-16, September.

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