generalized (jordan) derivations

In present paper, the stability of generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras for the generalized kind of Jensen-type functional equation is investigated. In fact, the main purpose of present paper is to prove the generalized Hyers-Ulam-Rassias stability of generalized Jordan derivation between algebra ${mathcal A}$ and an ${mathcal A}$-bimodule ${mathcal M}$. In present paper, the stability of generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras for the generalized kind of Jensen-type functional equation is investigated. In fact, the main purpose of present paper is to prove the generalized Hyers-Ulam-Rassias stability of generalized Jordan derivation between algebra ${mathcal A}$ and an ${mathcal A}$-bimodule ${mathcal M}$.

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begin If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems.the formula is not displayed correctly!