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A New Notion of Fuzzy Function Ideal Convergence

Author

Listed:
  • Dimitrios Georgiou

    (Department of Mathematics, University of Patras, 265 00 Patras, Greece
    These authors contributed equally to this work.)

  • Georgios Prinos

    (Department of Mathematics, University of Patras, 265 00 Patras, Greece
    These authors contributed equally to this work.)

Abstract

P.M. Pu and Y.M. Liu extended Moore-Smith’s convergence of nets to fuzzy topology and Y.M. Liu provided analogous results to J. Kelley’s classical characterization theorem of net convergence by introducing the notion of fuzzy convergence classes. In a previous paper, the authors of this study provided modified versions of this characterization by using an alternative notion of convergence of fuzzy nets, introduced by B.M.U. Afsan, named fuzzy net ideal convergence. Our main scope here is to generalize and simplify the preceding results. Specifically, we insert the concept of a fuzzy function ideal convergence class, L , on a non-empty set, X , consisting of triads ( f , e , I ) , where f is a function from a non-empty set, D , to the set FP ( X ) of fuzzy points in X , which we call fuzzy function, e ∈ FP ( X ) , and I is a proper ideal on D , and we provide necessary and sufficient conditions to establish the existence of a unique fuzzy topology, δ , on X , such that ( f , e , I ) ∈ L iff f I -converges to e , relative to the fuzzy topology δ .

Suggested Citation

  • Dimitrios Georgiou & Georgios Prinos, 2024. "A New Notion of Fuzzy Function Ideal Convergence," Mathematics, MDPI, vol. 12(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:260-:d:1318363
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    References listed on IDEAS

    as
    1. Agata Caserta & Giuseppe Di Maio & Ljubiša D. R. Kočinac, 2011. "Statistical Convergence in Function Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-11, December.
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