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Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Author

Listed:
  • Kandhasamy Tamilvanan

    (Department of Mathematics, Faculty of Science & Humanities, R.M.K. Engineering College, Kavaraipettai, Tiruvallur 601206, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61421, Saudi Arabia
    These authors contributed equally to this work.)

  • Jyotsana Jakhar

    (Department of Mathematics, M.D. University, Rohtak 124001, Haryana, India
    These authors contributed equally to this work.)

  • Renu Chugh

    (Department of Mathematics, M.D. University, Rohtak 124001, Haryana, India
    These authors contributed equally to this work.)

  • Jagjeet Jakhar

    (Department of Mathematics, Central University of Haryana, Mahendergarh 123031, Haryana, India
    These authors contributed equally to this work.)

  • John Michael Rassias

    (Pedagogical Department of Mathematics and Informatics, The National and Kapodistrian University of Athens, 15342 Attikis, Greece
    These authors contributed equally to this work.)

Abstract

In this work, we investigate the refined stability of the additive, quartic, and quintic functional equations in modular spaces with and without the Δ 2 -condition using the direct method (Hyers method). We also examine Ulam stability in 2-Banach space using the direct method. Additionally, using a suitable counterexample, we eventually demonstrate that the stability of these equations fails in a certain case.

Suggested Citation

  • Kandhasamy Tamilvanan & Ali H. Alkhaldi & Jyotsana Jakhar & Renu Chugh & Jagjeet Jakhar & John Michael Rassias, 2023. "Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces," Mathematics, MDPI, vol. 11(2), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:371-:d:1031296
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    References listed on IDEAS

    as
    1. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    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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    Cited by:

    1. Yahya Almalki & Balaanandhan Radhakrishnan & Uma Jayaraman & Kandhasamy Tamilvanan, 2023. "Some Common Fixed Point Results in Modular Ultrametric Space Using Various Contractions and Their Application to Well-Posedness," Mathematics, MDPI, vol. 11(19), pages 1-18, September.

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