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Fuzzy Stability Results of Generalized Quartic Functional Equations

Author

Listed:
  • Sang Og Kim

    (School of Data Science, Hallym University, Chuncheon 24252, Korea)

  • Kandhasamy Tamilvanan

    (Department of Mathematics, Government Arts College for Men, Krishnagiri 635 001, India)

Abstract

In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable.

Suggested Citation

  • Sang Og Kim & Kandhasamy Tamilvanan, 2021. "Fuzzy Stability Results of Generalized Quartic Functional Equations," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:120-:d:476413
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    References listed on IDEAS

    as
    1. Yang-Hi Lee, 2019. "On the Hyers-Ulam-Rassias Stability of a General Quintic Functional Equation and a General Sextic Functional Equation," Mathematics, MDPI, vol. 7(6), pages 1-14, June.
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    Cited by:

    1. Kandhasamy Tamilvanan & Abdulaziz Mohammed Alanazi & John Michael Rassias & Ali H. Alkhaldi, 2021. "Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces," Mathematics, MDPI, vol. 9(23), pages 1-16, November.
    2. Syed Abdul Mohiuddine & Kandhasamy Tamilvanan & Mohammad Mursaleen & Trad Alotaibi, 2022. "Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods," Mathematics, MDPI, vol. 10(11), pages 1-22, June.

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