Hyers-Ulam stability of horn-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: parallel to f(a + b) - f(a) - f(b)parallel to <= parallel to s(1) (f(a + b) + f(a - b) - 2f(a))parallel to (0.1) +parallel to s(2) (2f(a + b/2) - f(a) - f(b))parallel to, where s(1) and s(2) are fixed nonzero complex numbers with -root 2 vertical bar s(1)vertical bar + vertical bar s(2)vertical bar < 1.