Approximate ternary Jordan derivations on Banach ternary algebras

Let A be a Banach ternary algebra over a scalar field R or C and X be a ternary Banach A-module. A linear mapping D:(A,[ ](A))->(X,[ ](X)) is called a ternary Jordan derivation if D([xxx](A))=[D(x)xx](X)+[xD(x)x](X)+[xxD(x)](X) for all x is an element of A. In this paper, we investigate ternary Jordan derivations on Banach ternary algebras, associated with the following functional equation f((x+y+z)/4)+f((3x-y-4z)/4)+f((4x+3z)/4)=2f(x). Moreover, we prove the generalized Ulam-Hyers stability of ternary Jordan derivations on Banach ternary algebras.