There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.
设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.
本文总结作者们各自发表的一些关于优选法的理论结果,谨以此纪念著名的数学家华罗庚教授。§1 单峰函数类对 f:(0,1)→R,若存在 x_f∈(0,1),使 f 在区间(0,x_f〕中单调增加而在〔x_f,1)中单调减小,则说 f 是一个单峰函数,其全体记作 F。对 f∈F,以及包含 f 所求极值点 x_f
