Stability of an Alternative Functional Equation Related to the Quadratic Equation

Srisawat, Choodech; Trachoo, Kamonchat

doi:10.28924/2291-8639-24-2026-102

Research Article

Stability of an Alternative Functional Equation Related to the Quadratic Equation

Choodech Srisawat
Kamonchat Trachoo*

* Corresponding author

Abstract

Given a rational number $\alpha \ne \pm 2$, a criterion is established for the existence of the general solution to the alternative quadratic functional equation of the form
$f(xy) + f(xy^{-1}) = 2(f(x) + f(y))$ or $f(xy) + f(xy^{-1}) = \alpha(f(x) + f(y)),$
where $f$ is a mapping from an abelian group $(G,\cdot)$ to a uniquely divisible abelian group $(H,+)$. Subsequently, the Hyers-Ulam stability of this equation is proved for mappings from an abelian group to a Banach space, provided that $\alpha \notin \{0, \pm\frac{1}{2}, \pm 1, \pm 2\}$ is a rational number.

How to Cite

C. Srisawat, K. Trachoo, Stability of an Alternative Functional Equation Related to the Quadratic Equation, Int. J. Anal. Appl. 24 (2026), 102. https://doi.org/10.28924/2291-8639-24-2026-102

BibTeX

@article{Srisawat2026,
  author  = {Srisawat, Choodech and Trachoo, Kamonchat},
  title   = {Stability of an Alternative Functional Equation Related to the Quadratic Equation},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {102},
  doi     = {10.28924/2291-8639-24-2026-102}
}

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