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We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation f x 2y − f x − 2y 2 f x y − f x − y 2f 3y − 6f 2y 6f y .

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Abstract. In this note, we prove the Hyers-Ulam-Rassias stability of Jordan homomorphisms in C * −ternary algebras for the following generalized CauchyJensen additive mapping:and generalize some results concerning this functional equation.