On a coefficient body for concave functions
On a coefficient body for concave functions
复制标题
关于凹函数的系数体
DOI：
10.1007/s40315-013-0018-y
复制
发表时间：
2013
影响因子：
2.1
通讯作者：
Rintaro Ohno and Hiroshi Yanagihara
中科院分区：
文献类型：
--
作者：
K.Mitani;K.-S.Saito;Y.Takahashi;Rintaro Ohno and Hiroshi Yanagihara
设单位圆盘上的亚纯函数和单叶函数的简单极点是凸的。这些所谓的凹函数可以展开为$$\Begin{aligned}f(Z)=\sum_{n=0}^{\inty}a_n(F)z^n，\quad|z|<；p\end{aligned}$或$$\Begin{aligned}f(Z)=\sum_{n=-1}^{inty}c_n(F)(z-p)^n，\quad|z-p|<；1-p。给出了用正实部函数表示类函数的一个公式，并对系数体$$\Begin{Align}\Left\a_1(F)，c_{-1}(F)，c_1(F)\Right给出了明确的刻画.\结束{已对齐}$$
Forletbe the class of meromorphic and univalent functionsin the unit diskwith a simple pole atsuch thatis convex. These so-called concave functions can be expanded as $$\begin{aligned} f(z)= \sum _{n=0}^{\infty } a_n(f)z^n, \quad |z|<p \end{aligned}$$or $$\begin{aligned} f(z)= \sum _{n=-1}^{\infty } c_n(f) (z-p)^n, \quad |z-p|<1-p. \end{aligned}$$The present article shows a representation formula for functions of class, using functions of positive real part, and gives an explicit description of the coefficient body $$\begin{aligned} \left\{ a_1(f), c_{-1}(f), c_1(f) \right\} . \end{aligned}$$