Let A be a subalgebra of B(X) containing the identity operator I and an idem-potent P. Suppose that Let A be a subalgebra of B(X) containing the identity operator I and an idem-potent P. Suppose that α, β : A → A are ring epimorphisms and there exists some nest N on X such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A →B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →B(X) such that δ(A) =τ (A) + α(A)δ(I) for all A ∈ A. It is also shown that if δ is generalized (α, β)-derivable at zero point, then δis an additive generalized (α, β)-derivation. Moreover,
by use of this result, the additive maps (generalized) (α, β)-derivable at zero point on several nest algebras, are also characterized.
