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Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability

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  • Ravinder Kumar Sharma
  • Sumit Chandok
  • Bikash Koli Dey

Abstract

In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3-variables quadratic functional equation in the setting of 2-Banach space. Also, we obtain some hyperstability results for the 3-variables quadratic functional equation. The results obtained in this paper extend several known results of the literature to the setting of 2-Banach space.

Suggested Citation

  • Ravinder Kumar Sharma & Sumit Chandok & Bikash Koli Dey, 2023. "Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2023, pages 1-15, March.
    • Handle: RePEc:hin:jijmms:1721273
    DOI: 10.1155/2023/1721273
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