中文摘要：

Banach空间中线性算子的度量广义逆扰动定理具有重要应用，引入关注．在Acta Math Sinica Engrish Series，2014（7）中对于从Banach空间X到Banach空间Y，的有界线性算子T，在T的值域R（T）为切比雪夫子空间，T的零空间N（T）为切比雪夫子空间，且度量投影πN（T）为线性的条件下，得到二个有关非线性的广义逆扰动定理．本文证得：上述扰动定理结论的条件无需假定πN（T）的线性，只需假定Ⅳ（T），R（T）分别为X，Y中的切比雪夫子空间即可．

英文摘要：

There are some important applications for the perturbation theorem of metric generalized inverses of linear operators in Banach spaces, which topic is paid high attention. In Acta. Math. Sinica. English Series,2014（7） T is a bounded linear operator, under the conditions that the range R（T） of T is chebyshev subspace, the null space N（T） of T is chebyshev subspace and the metric projector πN（T） is linear, we obtain two theorems for perturbations of nonlinear generalized inverses. To the above theorem, we now only assume that N（T） and R（T） are chebyshev subspaces without the assumption of the linear property of πN（T）.