Banach空间中F-可微映照的不动点集

The Fixed Point Set for F-differentiable Maps in the Banach Space

设X是一个严格凸的复Banach空间,B是其单位球,f:B→B是F-可微映照,Df(0)是f在0点的Fréchet导算子。如果f(0)=0,则f与线性算子Df(0)在B内有完全相同的不动点,特别地,f的不动点集F(f)是仿射集。

Let X be a strictly convex complex Banach space, B be its unit ball and f: B→B be F-differentiable, if f(0)=0, then f has the same fixed point set with Dr(0) in B. In particular, the fixed point set for f is ffine.