Let A be an algebra and M be an A-bimodule. Let X be in A and \delta and \tau be linear maps from A into M which satisfies \delta(ab)=\delta(a)b+a\tau(b) and tau(ab)=tau(a)b+atau(b) for all a,b in A with ab = X. It is shown that \delta is a generalized Jordan derivation if \delta is continuous and X is left (or right) invertible. Also, it is shown that \delta is a generalized derivation if X is idempotent such that for m in M the condition XA(I − X)m = 0 implies (I − X)m = 0 and the condition mXA(I − X) = 0 implies mX = 0.
