摘要
设S为单位园盘内的正规单叶函数类。若f(z)=z+a_2z^2+a_3z^3+…∈S则当λ∈[0,1]时,Fekete和Szeg(?)证明了著名的结果(?)|a_3-λa_2~2|=1+2exp(-(2λ/(1-λ))) 本文考虑了S的一个子类凸函数类C,证明了不等式和-1/2≤|a_3|-|a_2|≤1/3对f∈C成立。
Let S be the class of normalized univalent functions in the unit disk. If f(z)=z+a_2z^2+a_3z^3+…∈S, Feket and Szego proved the well—known result
(?)|a_3-λa_2~2|=1+2exp(-(2λ/(1-λ))) for λ∈[0,1]. In this paper the corresponding problem is considered for the class C of eonvx functions, a subclass of S. It is shown that the sharp inequalities and
(-1/2)≤|a_3|-|a_2|≤(1/3) are valid for f∈C.
