Hom-derivations in Banach Algebras

초록

In this paper, we introduce hom-derivations in complex Banach algebras. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of hom-derivations in complex Banach algebras, associated with the bi-additive s-functional inequality ∥ f (x + y, z − w) + f (x − y, z + w) − 2 f (x, z) + 2 f (y, w)∥ ≤ ∥s(2 f( x+y,z−w) + 2 f( x−y,z+w) − 2 f (x, z) + 2 f (y, w)) ∥, 2 2 where s is a fixed nonzero complex number with |s| < 1.

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