title: Asymptotic aspect of derivations in Banach algebras.
abstract: We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
authors.affiliation: Department of Mathematical Finance and Information Statistics, Hallym University, 1 Hallymdaehakggil, Chuncheon, 24252 Korea.
authors.forename: Jaiok
authors.initials: J
authors.lastname: Roh
authors.affiliation: Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon, 34134 Korea.
authors.forename: Ick-Soon
authors.initials: IS
authors.lastname: Chang
keywords: Banach algebra; derivation; inequality; radical range; stability