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Fixed Point Technique: Stability Analysis of Quadratic Functional Equation in Various Quasi‐Banach Spaces

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  • Kandhasamy Tamilvanan
  • Faruk Özger
  • S. A. Mohiuddine
  • Naeem Ahmad
  • Masho Jima Kabeto

Abstract

In this present work, we derive the solution of a quadratic functional equation and investigate the Ulam stability of this equation in Banach spaces using fixed point and direct techniques. Mainly, we examine the stability results in quasi‐β‐Banach spaces and quasi‐fuzzy β‐Banach spaces by means of direct method as well as quasi‐Banach spaces by means of alternative fixed point theorem in the sense of generalized b‐metric spaces. To further establish the instability of a single case, an appropriate counterexample is also provided.

Suggested Citation

  • Kandhasamy Tamilvanan & Faruk Özger & S. A. Mohiuddine & Naeem Ahmad & Masho Jima Kabeto, 2025. "Fixed Point Technique: Stability Analysis of Quadratic Functional Equation in Various Quasi‐Banach Spaces," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:6689441
    DOI: 10.1155/jom/6689441
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    References listed on IDEAS

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    1. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    2. Heejeong Koh & Dongseung Kang, 2013. "Solution and Stability of Euler‐Lagrange‐Rassias Quartic Functional Equations in Various Quasinormed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Heejeong Koh & Dongseung Kang, 2013. "Solution and Stability of Euler-Lagrange-Rassias Quartic Functional Equations in Various Quasinormed Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, October.
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