On approximate derivations

Let A(1) be a subalgebra of a Banach algebra A and let f : A(1) --> A satisfies parallel to f(x + y) -f(x) -f(y)parallel to <= delta and parallel to f(x . y) - x . f(y) - f(x) . y parallel to <= epsilon, for all x, y is an element of A(1) and for some constants delta, epsilon >= 0. Then we prove that there exists a unique derivation d: A(1) --> A such that parallel to f(x) - d(x)parallel to <= delta, x is an element of A(1) and x . (f(y) - d(y)) = 0, x, y is an element of A(1). Moreover, we also prove the Rassias type stability result for derivations.