Farid (1991) has given an estimate for the norm of a perturbation V required to obtain an eigenvector for the perturbed operator T + V within a given ball centered at a given eigenvector of the unperturbed (closed linear) operator T. A similar result is derived from a more general result of the author (1989) which also guarantees that the corresponding eigenvalue is simple and also that the eigenpair is the limit of a sequence obtained in an iterative manner. © 1995 American Mathematical Society.