| Title:
|
Applications of the Hadamard product in geometric function theory (English) |
| Author:
|
Jakubowski, Zbigniew Jerzy |
| Author:
|
Liczberski, Piotr |
| Author:
|
Żywień, Łucja |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
148-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]). (English) |
| Keyword:
|
Hadamard product |
| Keyword:
|
typically real functions |
| Keyword:
|
class of type $A_\alpha$ |
| MSC:
|
30C80 |
| MSC:
|
30C99 |
| idZBL:
|
Zbl 0732.30018 |
| idMR:
|
MR1111999 |
| DOI:
|
10.21136/MB.1991.126141 |
| . |
| Date available:
|
2009-09-24T20:44:19Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126141 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| . |
