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Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods

Author

Listed:
  • Syed Abdul Mohiuddine

    (Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Kandhasamy Tamilvanan

    (Department of Mathematics, School of Advanced Sciences, Kalasalingam Academy of Research and Education, Srivilliputhur, Virudhunagar 626126, Tamil Nadu, India)

  • Mohammad Mursaleen

    (Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40402, Taiwan
    Department of Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India)

  • Trad Alotaibi

    (Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia)

Abstract

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate the stability results by using the Hyers method in modular space for quartic functional equations without using the Fatou property, without using the Δ b -condition and without using both the Δ b -condition and the Fatou property. Moreover, we investigate the stability results for this functional equation with the help of a fixed-point technique involving the idea of the Fatou property in modular spaces. Furthermore, a suitable counter example is also demonstrated to prove the non-stability of a singular case.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1938-:d:832330
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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. Sang Og Kim & Kandhasamy Tamilvanan, 2021. "Fuzzy Stability Results of Generalized Quartic Functional Equations," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
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    Cited by:

    1. 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.
    2. 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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