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Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ -2-Normed Spaces and Non-Archimedean Banach Spaces

Author

Listed:
  • Kandhasamy Tamilvanan

    (Department of Mathematics, Faculty of Science & Humanities, R.M.K. Engineering College, Srivilliputhur 601 206, Tamil Nadu, India)

  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61421, Saudi Arabia)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A & M University-Kingsville, 700 University Blvd., Kingsville, TX 78363-8202, USA)

  • Abdulaziz M. Alanazi

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ -2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

Suggested Citation

  • Kandhasamy Tamilvanan & Ali H. Alkhaldi & Ravi P. Agarwal & Abdulaziz M. Alanazi, 2023. "Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ -2-Normed Spaces and Non-Archimedean Banach Spaces," Mathematics, MDPI, vol. 11(2), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:270-:d:1025364
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    References listed on IDEAS

    as
    1. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    2. Soon-Mo Jung & Dorian Popa & Michael Rassias, 2014. "On the stability of the linear functional equation in a single variable on complete metric groups," Journal of Global Optimization, Springer, vol. 59(1), pages 165-171, May.
    3. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    4. Mohiuddine, S.A. & Danish Lohani, Q.M., 2009. "On generalized statistical convergence in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1731-1737.
    Full references (including those not matched with items on IDEAS)

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