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Fuzzy Continuous Mappings on Fuzzy F-Spaces

Author

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  • Sorin Nădăban

    (Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Drăgoi 2, RO-310330 Arad, Romania)

Abstract

In the present paper, we first introduce different types of fuzzy continuity for mappings between fuzzy F-normed linear spaces and the relations between them are investigated. Secondly, the principles of fuzzy functional analysis are established in the context of fuzzy F-spaces. More precisely, based on the fact that fuzzy continuity and topological continuity are equivalent, we obtain the closed graph theorem and the open mapping theorem. Using Zabreiko’s lemma, we prove the uniform bounded principle and Banach–Steinhaus theorem. Finally, some future research directions are presented.

Suggested Citation

  • Sorin Nădăban, 2022. "Fuzzy Continuous Mappings on Fuzzy F-Spaces," Mathematics, MDPI, vol. 10(20), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3746-:d:939676
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    References listed on IDEAS

    as
    1. Bînzar, Tudor & Pater, Flavius & Nădăban, Sorin, 2020. "Fuzzy bounded operators with application to Radon transform," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Bivas Dinda & Santanu Kumar Ghosh & T. K. Samanta, 2019. "Intuitionistic Fuzzy Pseudo-Normed Linear Spaces," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 113-127, March.
    3. Sadeqi, I. & Kia, F. Solaty, 2009. "Fuzzy normed linear space and its topological structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2576-2589.
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