| Title:
|
Extreme points of subordination and weak subordination families of harmonic mappings (English) |
| Author:
|
Qiao, Jinjing |
| Author:
|
Wang, Xiantao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
145-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of the paper is to discuss the extreme points of subordination and weak subordination families of harmonic mappings. Several necessary conditions and sufficient conditions for harmonic mappings to be extreme points of the corresponding families are established. (English) |
| Keyword:
|
planar harmonic mapping |
| Keyword:
|
extreme point |
| Keyword:
|
subordination |
| Keyword:
|
weak subordination |
| Keyword:
|
class $N$ |
| MSC:
|
30C20 |
| MSC:
|
30C45 |
| MSC:
|
30C65 |
| idZBL:
|
Zbl 1224.30111 |
| idMR:
|
MR2782765 |
| DOI:
|
10.1007/s10587-011-0003-4 |
| . |
| Date available:
|
2011-05-23T12:37:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141524 |
| . |
| Reference:
|
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| Reference:
|
[2] Abu-Muhanna, Y., Hallenbeck, D. J.: Subordination families and extreme points.Trans. Amer. Math. Soc. 308 (1988), 83-89. Zbl 0651.30019, MR 0946431, 10.1090/S0002-9947-1988-0946431-1 |
| Reference:
|
[3] Dihan, N. A.: Some subordination results and coefficient estimates for certain classes of analytic functions.Mathematica 49 (2007), 3-12. Zbl 1174.30005, MR 2364024 |
| Reference:
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| Reference:
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| Reference:
|
[6] Duren, P.: Harmonic Mappings in the Plane.Cambridge university Press, New York (2004). Zbl 1055.31001, MR 2048384 |
| Reference:
|
[7] Hallenbeck, D. J., Hallenbeck, K. T.: Classes of analytic functions subordinate to convex functions and extreme points.J. Math. Anal. Appl. 282 (2003), 792-800. Zbl 1025.30011, MR 1989687, 10.1016/S0022-247X(03)00257-9 |
| Reference:
|
[8] Hallenbeck, D. J., Macgregor, T. H.: Subordination and extreme-point theory.Pacific J. Math. 50 (1974), 455-468. Zbl 0258.30015, MR 0361035, 10.2140/pjm.1974.50.455 |
| Reference:
|
[9] MacGregor, T. H.: Applications of extreme-point theory to univalent functions.Michigan Math. J. 19 (1972), 361-376. Zbl 0257.30017, MR 0311885, 10.1307/mmj/1029000948 |
| Reference:
|
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| Reference:
|
[11] Ryff, J. V.: Subordinate $H^p$ functions.Duke Math. J. 33 (1966), 347-354. MR 0192062, 10.1215/S0012-7094-66-03340-0 |
| Reference:
|
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| Reference:
|
[13] Srivastava, H. M., Sümer, E. Sevtap: Some applications of a subordination theorem for a class of analytic functions.Appl. Math. Lett. 21 (2008), 394-399. MR 2406520, 10.1016/j.aml.2007.02.032 |
| Reference:
|
[14] Tkaczyńska, K.: On extreme points of subordination families with a convex majorant.J. Math. Anal. Appl. 145 (1990), 216-231. MR 1031186, 10.1016/0022-247X(90)90442-I |
| Reference:
|
[15] Lin, Z.: Subordination of analytic functions.Chinese Acta. Sci. Natur. Univ. Sunyatseni 29 (1990), 44-48. MR 1075847 |
| . |
