• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.149-161
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• 2010

We adopt the idea of $C{\breve{a}}dariu$ and Radu to prove the generalized Hyers-Ulam stability of generalized Jordan triple derivation in Banach algebra. In addition, we take account of problems for generalized Jordan triple linear derivation in Banach algebra.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.261-269
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• 2009

We adopt the idea of $C\check{a}dariu$ and Radu to prove the stability of Jordan triple linear derivations and we take account of the Jacobson radical range problem for linear derivations.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.277-283
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• 2022

Let 𝒜 be a unital Banach algebra, 𝓜 a unital 𝒜-bimodule, and 𝛿 a linear mapping from 𝒜 into 𝓜. We prove that if 𝛿 satisfies 𝛿(A)A^-1+A^-1𝛿(A)+A𝛿(A^-1)+𝛿(A^-1)A = 0 for every invertible element A in 𝒜, then 𝛿 is a Jordan derivation. Moreover, we show that 𝛿 is a Jordan derivable mapping at the unit element if and only if 𝛿 is a Jordan derivation. As an application, we answer the question posed in [4, Problem 2.6].