Lie triple and Jordan derivable mappings on nest algebras

Let ?? be a nontrivial nest on a Banach space X over the complex field C, assume that there exists a nontrivial element in ?? which is complemented in X. Let Alg??? be the associated nest algebra. In this article, we show that if d is a Lie triple derivable mapping from Alg??? into B(X) then for any A,?B???Alg??? there exists a ? A,B (depending on A and B) in C such that d(A?+?B)?=?d(A)?+?d(B)?+?? A,B I, and d?=?D?+?t, where D is an additive derivation from Alg??? into B(X) and t is a mapping from Alg??? into CI such that t(A?+?B)?=?t(A)?+?t(B)?+?? A,B I and t([[A,?B],?C])?=?0 for all A,?B,?C???Alg???. We also show that if d is a Jordan derivable mapping from Alg??? into B(X) then d is an additive derivation.