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We investigate Jordan ∗-derivations on C∗-algebras and Jordan ∗-derivations on JC∗-algebras associated with the following functional inequality ‖f(x)+f(y)+kf(z)‖≤‖kf((x+y)/k+z)‖ for some integer k greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan ∗-derivations on C∗-algebras and of Jordan ∗-derivations on JC∗-algebras associated with the following functional equation f((x+y)/k+z)=(f(x)+f(y))/k+f(z) for some integer k greater than 1

abstract and applied analysis

Jordan<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∗</mml:mo></mml:math>-Derivations on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math>-Algebras and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math>-Algebras

Jordan∗-Derivations onC∗-Algebras andJC∗-Algebras