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.
<正> 设Ω是 C 中含原点的有界对称域,用 b 记它的 silov 边界.Ω相对于原点是圆型的和星形的,b 是圆型的.用Γ记Ω的全纯自同构群,Γ_0为Γ的使原点不变的子群.b 上存在唯一的使Γ_0不变的测度λ,健λ(b)=1.〔1〕构造了一组齐次多项式{(?)}:k=0,1,…,u=1,2,…m,m_k=C_(n+k-1)~k,它们在Ω中是完备正交的,在 b 上是标准正交的.用 H(Ω)表示Ω上全纯函数的全体.f 的β(β>0)阶分数导数和分数积分定义为:
In this paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.
