| Title:
|
Some properties of certain subclasses of bounded Mocanu variation with respect to $2k$-symmetric conjugate points (English) |
| Author:
|
Aghalary, Rasoul |
| Author:
|
Kazemzadeh, Jafar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
191-202 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce subclasses of analytic functions of bounded radius rotation, bounded boundary rotation and bounded Mocanu variation with respect to $2k$-symmetric conjugate points and study some of its basic properties. (English) |
| Keyword:
|
$2k$-symmetric conjuqate points |
| Keyword:
|
bounded Mocanu variation |
| Keyword:
|
bounded radius rotation |
| Keyword:
|
bounded boundary rotation |
| MSC:
|
30C45 |
| MSC:
|
30C80 |
| idZBL:
|
Zbl 07088845 |
| idMR:
|
MR3974187 |
| DOI:
|
10.21136/MB.2018.0141-17 |
| . |
| Date available:
|
2019-06-21T11:34:18Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147759 |
| . |
| Reference:
|
[1] Eenigenberg, P., Miller, S. S., Mocanu, P. T., Reade, M. O.: On a Briot-Bouquet differential subordination.General Inequalities 3 International Series of Numerical Mathematics 64. Birkhäuser, Basel (1983), 339-348 E. F. Beckenbach et al. Zbl 0527.30008, MR 0785788, 10.1007/978-3-0348-6290-5_26 |
| Reference:
|
[2] Graham, I., Kohr, G.: Geometric Function Theory in One and Higher Dimensions.Pure and Applied Mathematics 255. Marcel Dekker, New York (2003). Zbl 1042.30001, MR 2017933, 10.1201/9780203911624 |
| Reference:
|
[3] Miller, S. S., Mocanu, P. T.: Differential Subordinations: Theory and Applications.Pure and Applied Mathematics 225. Marcel Dekker, New York (2000). Zbl 0954.34003, MR 1760285, 10.1201/9781482289817 |
| Reference:
|
[4] Noor, K. I.: On subclasses of close-to-convex functions of higher order.Int. J. Math. Math. Sci. 15 (1992), 279-289. Zbl 0758.30010, MR 1155521, 10.1155/S016117129200036X |
| Reference:
|
[5] Padmanabhan, K. S., Parvatham, R.: Properties of a class of functions with bounded boundary rotation.Ann. Pol. Math. 31 (1976), 311-323. Zbl 0337.30009, MR 0390199, 10.4064/ap-31-3-311-323 |
| Reference:
|
[6] Pinchuk, B.: Functions with bounded boundary rotation.Isr. J. Math. 10 (1971), 6-16. Zbl 0224.30024, MR 0301180, 10.1007/BF02771515 |
| Reference:
|
[7] Sakaguchi, K.: On a certain univalent mapping.J. Math. Soc. Japan. 11 (1959), 72-75. Zbl 0085.29602, MR 0107005, 10.2969/jmsj/01110072 |
| Reference:
|
[8] Wang, Z.-G., Gao, C.-Y.: On starlike and convex functions with respect to $2k$-symmetric conjugate points.Tamsui Oxf. J. Math. Sci. 24 (2008), 277-287. Zbl 1343.30014, MR 2456132 |
| Reference:
|
[9] Wang, Z.-G., Gao, C.-Y., Yuan, S.-M.: On certain subclasses of close-to-convex and quasi-convex functions with respect to $k$-symmetric points.J. Math. Anal. Appl. 322 (2006), 97-106. Zbl 1102.30015, MR 2238151, 10.1016/j.jmaa.2005.08.060 |
| . |
