PERTURBATION ANALYSIS OF BOUNDED HOMOGENEOUS GENERALIZED INVERSES ON BANACH SPACES

Let X, Y be Banach spaces and T: X -> Y be a bounded linear operator. In this paper, we initiate the study of the perturbation problems for bounded homogeneous generalized inverse T-h and quasi-linear projector generalized inverse T-H of T. Some applications to the representations and perturbations of the Moore-Penrose metric generalized inverse T-M of T are also given. The obtained results in this paper extend some well-known results for linear operator generalized inverses in this field.