"Hyers-Ulam stability of hom-derivations in Banach algebras"

Abstract

"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: \begin{eqnarray}\label{0.1} \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 $\sqrt{2}|s_{1}|+|s_{2}| < 1$."