Geodesic
Applications of the Hadamard product in geometric function theory
Mathematica Bohemica, Tome 116 (1991) no. 2, pp. 148-159

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Let $\Cal A$ denote the set of functions $F$ holomorphic in the unit disc, normalized clasically: $F(0)=0, F'(0)=1$, whereas $A\subset \Cal A$ is an arbitrarily fixed subset. In this paper various properties of the classes $A_\alpha, \alpha \in C \{-1,-\frac{1}{2},\ldots\}$, of functions of the form $f=F*k_\alpha$ are studied, where $F\in .A$, $k_\alpha(z)=k(z,\alpha)=z+\frac{1}{1+\alpha}z^2+\ldots + \frac{1}{1+(n-1)\alpha}z^n+\ldots$, and $F*k_\alpha$ denotes the Hadamard product of the functions $F$ and $k_\alpha$. Some special cases of the set $A$ were considered by other authors (see, for example, [15],[6],[3]).
Let $\Cal A$ denote the set of functions $F$ holomorphic in the unit disc, normalized clasically: $F(0)=0, F'(0)=1$, whereas $A\subset \Cal A$ is an arbitrarily fixed subset. In this paper various properties of the classes $A_\alpha, \alpha \in C \{-1,-\frac{1}{2},\ldots\}$, of functions of the form $f=F*k_\alpha$ are studied, where $F\in .A$, $k_\alpha(z)=k(z,\alpha)=z+\frac{1}{1+\alpha}z^2+\ldots + \frac{1}{1+(n-1)\alpha}z^n+\ldots$, and $F*k_\alpha$ denotes the Hadamard product of the functions $F$ and $k_\alpha$. Some special cases of the set $A$ were considered by other authors (see, for example, [15],[6],[3]).
DOI : 10.21136/MB.1991.126141
Classification : 30C80, 30C99
Keywords: Hadamard product; typically real functions; class of type $A_\alpha$ 
Jakubowski, Zbigniew Jerzy; Liczberski, Piotr; Żywień, Łucja. Applications of the Hadamard product in geometric function theory. Mathematica Bohemica, Tome 116 (1991) no. 2, pp. 148-159. doi: 10.21136/MB.1991.126141
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