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Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

Author

Listed:
  • Abdulaziz M. Alanazi

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
    These authors contributed equally to this work.)

  • G. Muhiuddin

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
    These authors contributed equally to this work.)

  • K. Tamilvanan

    (Department of Mathematics, Government Arts College (Men), Krishnagiri, Tamil Nadu 635 001, India
    These authors contributed equally to this work.)

  • Ebtehaj N. Alenze

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
    These authors contributed equally to this work.)

  • Abdelhalim Ebaid

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
    These authors contributed equally to this work.)

  • K. Loganathan

    (Department of Mathematics, Faculty of Engineering, Karpagam Academy of Higher Education, Coimbatore, Tamil Nadu 641 021, India
    These authors contributed equally to this work.)

Abstract

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.

Suggested Citation

  • Abdulaziz M. Alanazi & G. Muhiuddin & K. Tamilvanan & Ebtehaj N. Alenze & Abdelhalim Ebaid & K. Loganathan, 2020. "Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods," Mathematics, MDPI, vol. 8(7), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1050-:d:378241
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    References listed on IDEAS

    as
    1. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    2. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    3. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.
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    Cited by:

    1. Subramani Karthikeyan & Kandhasamy Tamilvanan & John Michael Rassias & Masho Jima Kabeto, 2025. "Thermal Applications of Stability Analysis of Cubic Functional Equation in Banach Spaces and Intuitionistic Fuzzy Normed Spaces," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    2. P. Agilan & Mohammed M. A. Almazah & K. Julietraja & Ammar Alsinai, 2023. "Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces," Mathematics, MDPI, vol. 11(3), pages 1-19, January.

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