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2008•arXiv (Cornell University)Open access

Nearly generalized Jordan derivations

M‎. ‎Eshaghi Gordji, N. Ghobadipour

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Abstract

Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C-$linear mapping $d:A \to X$ is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) $δ:A \to X$ such that $d(a^2)=ad(a)+δ(a)a$ for all $a \in A.$ The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

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Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C-$linear mapping $d:A \to X$ is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) $δ:A \to X$ such that $d(a^2)=ad(a)+δ(a)a$ for all $a \in A.$ The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

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Available abstract

Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C-$linear mapping $d:A \to X$ is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) $δ:A \to X$ such that $d(a^2)=ad(a)+δ(a)a$ for all $a \in A.$ The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

Key concepts: Bimodule, Mathematics, Stability (learning theory), Algebra over a field, Derivation, Pure mathematics, Computer science, Medicine

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