The Hyers-Ulam stability of ( α,β ) - derivations from a unital ring R to a R -bimodule which is a cone Banach space with the cone norm ||·||P , where P is a normal cone in a real Banach space E is investigated associated with the following functional equation
f (( a + b) c ) = f ( a ) α ( c ) + β ( a ) f ( c ) + f (b) α ( c ) + β (b) f ( c )
using the fixed point method and the direct method respectively.