- - - Department of Mathematics, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.
- - - Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
- - - Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas ۷۲۷۰۱, USA

Let A be a Banach ternary algebra over a scalar field \mathbb{R} or \mathbb{C} and X be a Banach ternary A-module. Let \sigma, \tau and \xi be linear mappings on A, a linear mapping D : (A,[ ]_A) \to (X, [ ]_X) is called a ternary (\sigma,\tau,\xi)-derivation, ifD([xyz]_A) = [D(x)\tau(y)\xi(z)]_X + [\sigma(x)D(y)\xi(z)]_X + [\sigma(x)\tau(y)D(z)]_Xfor all x,y, z \in A. In this paper, we investigate ternary (\sigma,\tau,\xi)-derivation on Banach ternary algebras, associated with the following functional equationf(\frac{x + y + z}{۴}) + f(\frac{۳x - y - ۴z}{۴}) + f(\frac{۴x + ۳z}{۴}) = ۲f(x).Moreover, we prove the generalized Ulam-Hyers stability of ternary (\sigma,\tau,\xi)-derivations on Banach ternary algebras.

Banach ternary algebra, Banach ternary A-module, Ternary (sigma,tau,xi)-derivation