| Title:
|
On an extremal problem (English) |
| Author:
|
Zyskowska, Krystyna |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
113-124 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and holomorphic in the unit disc $\varDelta= \{z |z| < 1\}$. In the paper we obtain a sharp estimate of the functional $|a_3 - \alpha a^2_2| + \alpha|a_2|^2$ in the class $S$ for an arbitrary $\alpha\in\Bbb R$. (English) |
| Keyword:
|
coefficient problems |
| Keyword:
|
Koebe function |
| Keyword:
|
univalent function |
| MSC:
|
30C50 |
| MSC:
|
30C70 |
| idZBL:
|
Zbl 0857.30016 |
| idMR:
|
MR1357596 |
| DOI:
|
10.21136/MB.1995.126223 |
| . |
| Date available:
|
2009-09-24T21:09:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126223 |
| . |
| Reference:
|
[1] L. Bieberbach: Über die Koeffizienten derjenigen Potenzreihen, welche schlichte Abbildung des Einheitskreises vermitteln.Preuss. Akad. deг Wiss. Sitzungsb. 38 (1916), 940-955. Berlin. |
| Reference:
|
[2] G. M. Goluzin: Some questions of the theory of univalent functions.Trudy Mat. Inst. Steklov 27 (1949), 51-56. (In Russian.) MR 0042510 |
| Reference:
|
[3] Z. J. Jakubowski K. Zyskowska: On an estimate of some functional in the class of holomorphic univalent functions.Mathematica Bohemica 118 (1993), 281-296. MR 1239123 |
| Reference:
|
[4] J. A. Jenkins: On certain coefficients on univalent functions.Princ. Univ. Press, New Jeгsey, 1960, pp. 159-194. MR 0117345 |
| Reference:
|
[5] W. Ma D. Minda: Uniformly convex functions II.To appear in Ann. Polon. Math. Zbl 0792.30008, MR 1244399 |
| Reference:
|
[6] A. C. Schaeffer D. C. Spencer: Coefficient regions for schlicht functions.Amer. Math. Soc., Colloq. Publ. 35 (1950), 36-37. MR 0037908 |
| . |
