ON STABILITY OF QUADRATIC LIE HOM-DERS IN LIE BANACH ALGEBRAS

Abstract

We study the notion of a quadratic Lie hom-der in a Lie Banach algebra associated with the functional equation f(x + y/2 +z)+ f(x + y/2 -z)+ f(x - y/2 +z)+ f(x - y/2 -z)= f (x)+ f (y)+4 f (z), which was first introduced by Park, Hong and Kim (2006). We also present a relation between the above functional equation and the quadratic functional equation on certain groups. Finally, we prove some stability results of the quadratic Lie hom-ders in Lie Banach algebras by using Hyers' direct method.