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Bihom derivations in Banach algebras

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In this paper, we introduce bihom derivations in complex Banach algebras. Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of bihom derivations in complex Banach algebras, associated with the bi-additive s-functional inequality \(\Vert f(x+y, z-w) + f(x-y, z+w) -2f(x,z)+2 f(y, w)\Vert \le \Vert s \left( 2f\left( \frac{x+y}{2}, z-w\right) + 2f\left( \frac{x-y}{2}, z+w\right) - 2f(x,z )+ 2 f(y, w)\right) \Vert \), where s is a fixed nonzero complex number with \(|s |< 1\).

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This work was supported by Incheon National University Research Grant 2018–2019.

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Correspondence to Choonkil Park.

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Hwang, I., Park, C. Bihom derivations in Banach algebras. J. Fixed Point Theory Appl. 21, 81 (2019).

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