• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.995-1004
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• 2000

In this paper we shall give a slight generalization of J. Vukman's Theorem. And show from the result that the image of a continuous linear Jordan derivation on a noncommutative Banach algebra A is contained in the radical under the condition [D(x),x]E(x) ${\in}$ rad(A) for all $x{\in}A$ . And we show some properties of the derivations on noncommutative Banach algebras.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.615-622
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• 2009

We solve the automatic continuity problem of an approximate higher derivation on a semisimple Banach algebra and investigate Hyers-Ulam stability for higher derivations.