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We investigate the Ulam stability and hyperstability of the functional equations \(\displaystyle \begin {array}{l} f\left (\frac {x-y}{2}+z\right )+ f\left (\frac {y-z}{2}+x\right )+ f\left (\frac {z-x}{2}+y\right )=f(x+y+z),\\ f\left (\frac {x-y}{2}+z\right )+ f\left (\frac {y-z}{2}+x\right )+ f\left (\frac {z-x}{2}+y\right )=f(x)+f(y)+f(z), \end {array} \) in Banach spaces and 2-Banach spaces.

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On Ulam Stability and Hyperstability of Functional Equations in Banach Spaces and 2-Banach Spaces

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  • 发表日期：

    2026年

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  • Abbas Najati,
  • Themistocles M. Rassias

摘要

We investigate the Ulam stability and hyperstability of the functional equations \(\displaystyle \begin {array}{l} f\left (\frac {x-y}{2}+z\right )+ f\left (\frac {y-z}{2}+x\right )+ f\left (\frac {z-x}{2}+y\right )=f(x+y+z),\\ f\left (\frac {x-y}{2}+z\right )+ f\left (\frac {y-z}{2}+x\right )+ f\left (\frac {z-x}{2}+y\right )=f(x)+f(y)+f(z), \end {array} \) in Banach spaces and 2-Banach spaces.