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Using the direct method, we prove the Hyers-Ulam stability of \(C^*\) -ternary biderivations and \(C^*\) -ternary bihomomorphism in \(C^*\) -ternary algebras, associated with the following bi-additive s-functional inequality: \(\displaystyle \begin {aligned}{} && \| f(x+y, z-w) + f(x-y, z+w) -2f(x,z)+2 f(y, w)\| \\ && \le \left \| s \left (2f\left (\frac {x+y}{2}, z-w\right) + 2f\left (\frac {x-y}{2}, z+w\right) - 2f(x,z)+ 2 f(y, w)\right)\right \|, \end {aligned} \) where s is a fixed nonzero complex number with \(|s |< 1\) .

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\(C^{\ast}\) -Ternary Biderivations and \(C^{\ast}\) -Ternary Bihomomorphisms

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  • 发表日期：

    2025年

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  • Jung Rye Lee,
  • Choonkil Park,
  • Michael Th. Rassias

摘要

Using the direct method, we prove the Hyers-Ulam stability of \(C^*\) -ternary biderivations and \(C^*\) -ternary bihomomorphism in \(C^*\) -ternary algebras, associated with the following bi-additive s-functional inequality: \(\displaystyle \begin {aligned}{} && \| f(x+y, z-w) + f(x-y, z+w) -2f(x,z)+2 f(y, w)\| \\ && \le \left \| s \left (2f\left (\frac {x+y}{2}, z-w\right) + 2f\left (\frac {x-y}{2}, z+w\right) - 2f(x,z)+ 2 f(y, w)\right)\right \|, \end {aligned} \) where s is a fixed nonzero complex number with \(|s |< 1\) .