Applications of the Hadamard product in geometric function theory

@article{Jakubowski1991,
abstract = {Let $\mathcal \{A\}$ denote the set of functions $F$ holomorphic in the unit disc, normalized clasically: $F(0)=0, F^\{\prime \}(0)=1$, whereas $A\subset \mathcal \{A\}$ is an arbitrarily fixed subset. In this paper various properties of the classes $A_\alpha , \alpha \in C \lbrace -1,-\frac\{1\}\{2\},\ldots \rbrace $, 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]).},
author = {Jakubowski, Zbigniew Jerzy, Liczberski, Piotr, Żywień, Łucja},
journal = {Mathematica Bohemica},
keywords = {Hadamard product; typically real functions; class of type $A_\alpha $; Hadamard product},
language = {eng},
number = {2},
pages = {148-159},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Applications of the Hadamard product in geometric function theory},
url = {http://eudml.org/doc/29295},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Jakubowski, Zbigniew Jerzy
AU - Liczberski, Piotr
AU - Żywień, Łucja
TI - Applications of the Hadamard product in geometric function theory
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 2
SP - 148
EP - 159
AB - Let $\mathcal {A}$ denote the set of functions $F$ holomorphic in the unit disc, normalized clasically: $F(0)=0, F^{\prime }(0)=1$, whereas $A\subset \mathcal {A}$ is an arbitrarily fixed subset. In this paper various properties of the classes $A_\alpha , \alpha \in C \lbrace -1,-\frac{1}{2},\ldots \rbrace $, 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]).
LA - eng
KW - Hadamard product; typically real functions; class of type $A_\alpha $; Hadamard product
UR - http://eudml.org/doc/29295
ER -