carpathian_2022_38_3_837_844_001

Hyers-Ulam stability of hom-derivations in Banach algebras

 Mouktonglang, Thanasak, Suparatulatorn, Raweerote and Park, Choonkil

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carpathian_2022_38_3_837_844

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In this work, we prove the Hyers–Ulam stability of hom-derivations in complex Banach algebras, associated with the additive (s_{1}, s_{2})-functional inequality:

(1)   \begin{eqnarray*} \nonumber \| f(a+b) - f(a) - f(b)\| &\le& \left \|s_{1} \left(f(a+b) + f(a-b)-2f(a)\right)\right\| \\ &\quad& + \left \|s_{2} \left(2f\left( \frac{a+b}{2}\right) - f(a) - f(b)\right)\right\|, \end{eqnarray*}

where s_{1} and s_{2} are fixed nonzero complex numbers with \sqrt{2}|s_{1}|+|s_{2}| < 1.

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Author(s)

 Mouktonglang, Thanasak,  Suparatulatorn, Raweerote, Park, Choonkil
DOI

https://doi.org/10.37193/CJM.2022.03.26

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