关于Gelfer函数

On Gelfer Functions

我们称单位圆盘中的解析函数f(z)=1+(sum from n=1 to ∞)a_nZ^n为Gelfer函数,如果对一切Z,∈△,都有f(z)+f(C)≠0。文〔1〕中关于Gelfer函数提出了若干问题,我们解决了其中的两个。

Let G be the class of Gclfcr functions f which are analytic in the unit disc △ = {|z| < 1} and satis fying conditions f(0)= 1 and f(z)+f(ξ)≠0 for all z,ξ ∈ △. Recently, S.Yamashita [1] posed some prob-lems for Gelfer functions. In this paper, we answer two of them.