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

Issue no: Vol 38/2022 no. 3 Tags: fixed point method, direct method, Hyers-Ulam stability, hom-derivation in Banach algebra

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