Stability of ternary m-derivations over Banach ternary modules

In this paper we introduce Banach ternary modules over Banach ternary algebras and using fixed point methods, we prove the stability of ternary additive, quadratic, cubic and quartic derivations in such modules for the functional equation [(f(ax + y) + f(ax − y) = a^{m−2}[f(x + y) + f(x − y)$ + 2(a2 − 1)[am−2f(x) + (m − 2)(1 − (m − 2)2) 6 f(y)]. for each m = 1, 2, 3, 4.