| Title:
|
A note on Briot-Bouquet-Bernoulli differential subordination (English) |
| Author:
|
Kanas, Stanisława |
| Author:
|
Kowalczyk, Joanna |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
339-347 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p, q$ be analytic functions in the unit disk $\Cal U$. For $\alpha \in [0,1)$ the authors consider the differential subordination and the differential equation of the Briot-Bouquet type: $$ p^{1-\alpha}(z)+\frac{zp'(z)}{\delta p^{\alpha}(z) + \lambda p(z)}\prec h(z), \quad z\in \Cal U, $$ $$ q^{1-\alpha}(z)+\frac{nzq'(z)}{\delta q^{\alpha}(z)+\lambda q(z)} = h(z),\quad z\in \Cal U, $$ with $p(0) =q(0) =h(0)=1$. The aim of the paper is to find the dominant and the best dominant of the above subordination. In addition, the authors give some particular cases of the main result obtained for appropriate choices of functions $h$. (English) |
| Keyword:
|
differential subordinations |
| Keyword:
|
Briot-Bouquet-Bernoulli differential sub\-or\-di\-na\-tion |
| MSC:
|
30C35 |
| MSC:
|
30C45 |
| MSC:
|
30C80 |
| MSC:
|
34A25 |
| idZBL:
|
Zbl 1121.34004 |
| idMR:
|
MR2176896 |
| . |
| Date available:
|
2009-05-05T16:51:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119528 |
| . |
| Reference:
|
[1] Miller S.S., Mocanu P.T.: Differential subordinations and univalent functions.Michigan Math. J. 28 (1981), 157-171. Zbl 0439.30015, MR 0616267 |
| Reference:
|
[2] Miller S.S., Mocanu P.T.: Univalent solutions of Briot-Bouquet differential equations.J. Differential Equations 56 3 (1985), 297-309. Zbl 0507.34009, MR 0780494 |
| Reference:
|
[3] Miller S.S., Mocanu P.T.: The theory and applications of second-order differential subordinations.Studia Univ. Babeş-Bolyai Math. 34 4 (1989), 3-33. Zbl 0900.30031, MR 1073534 |
| Reference:
|
[4] Miller S.S., Mocanu P.T.: Differential Subordinations. Theory and Applications.Marcel Dekker, Inc, New York, Basel, 2000. Zbl 0954.34003, MR 1760285 |
| Reference:
|
[5] Mocanu P.T.: Convexity of some particular functions.Studia Univ. Babeş-Bolyai Math. 29 (1984), 70-73. Zbl 0548.30006, MR 0782294 |
| . |
