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Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

Author

Listed:
  • P. Agilan

    (Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India)

  • Mohammed M. A. Almazah

    (Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
    Department of Mathematics and Computer, College of Sciences, Ibb University, Ibb 70270, Yemen)

  • K. Julietraja

    (Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India)

  • Ammar Alsinai

    (Department of Mathematics, University of Mysore, Manasagangotri, Mysore 570015, Karnataka, India)

Abstract

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:681-:d:1050272
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    References listed on IDEAS

    as
    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. Emanuel Guariglia & Kandhasamy Tamilvanan, 2020. "On the stability of radical septic functional equations," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    3. 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.
    4. P. Saha & T. K. Samanta & Pratap Mondal & B. S. Choudhury & Manuel De La Sen, 2020. "Applying Fixed Point Techniques to Stability Problems in Intuitionistic Fuzzy Banach Spaces," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
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    Cited by:

    1. Reza Chaharpashlou & Reza Saadati & António M. Lopes, 2023. "Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations," Mathematics, MDPI, vol. 11(9), pages 1-11, May.

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