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We investigate the Hyers-Ulam-Rassias stability and hyperstability of the functional equations \(\begin{aligned} f\left[ g(x+\lambda y)\right] &=f(x)+f(y),\\ f\left[ g(x+\lambda y)\right] +f\left[ g(x-\lambda y)\right] &=2f(x)+2\lambda ^2f(y),\\ f\left[ g(x+\lambda y)\right] +f\left[ g(x-\lambda y)\right] &=2f(x)+\lambda ^2[f(y)+f(-y)], \end{aligned}\) in Banach spaces.

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On Hyers-Ulam-Rassias Stability and Hyperstability of Generalized Affine, Quadratic and Drygas Functional Equations

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  • 发表日期：

    2026年

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  • Abbas Najati,
  • Jafar Mohammadpour,
  • Themistocles M. Rassias

摘要

We investigate the Hyers-Ulam-Rassias stability and hyperstability of the functional equations \(\begin{aligned} f\left[ g(x+\lambda y)\right] &=f(x)+f(y),\\ f\left[ g(x+\lambda y)\right] +f\left[ g(x-\lambda y)\right] &=2f(x)+2\lambda ^2f(y),\\ f\left[ g(x+\lambda y)\right] +f\left[ g(x-\lambda y)\right] &=2f(x)+\lambda ^2[f(y)+f(-y)], \end{aligned}\) in Banach spaces.