Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces

Let $X,Y$ be Banach spaces and $T:X\to Y$ 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.