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Extremal problems on the class of convex functions of order-1/2

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成果类型:
期刊论文
作者:
Abu Muhanna, Yusuf*;Li, Liulan;Ponnusamy, Saminathan
通讯作者:
Abu Muhanna, Yusuf
作者机构:
[Abu Muhanna, Yusuf] Amer Univ Sharjah, Dept Math, Sharjah 26666, U Arab Emirates.
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.
[Ponnusamy, Saminathan] SETS, Indian Stat Inst, Chennai Ctr, Madras 600113, Tamil Nadu, India.
通讯机构:
[Abu Muhanna, Yusuf] A
Amer Univ Sharjah, Dept Math, Sharjah 26666, U Arab Emirates.
语种:
英文
关键词:
Univalent;Convex;Starlike;Close-to-convex;Extreme points;Hayman index;Arclength;Zalcman functional;and Harmonic function
期刊:
Archiv der Mathematik
ISSN:
0003-889X
年:
2014
卷:
103
期:
6
页码:
461-471
基金类别:
Acknowledgements. The visit and the research of the first author was supported by the “Abel visiting Scholar Program” of the Commission for Developing Countries (IMU). The research was also supported by the NSF of China (No. 11201130), the Hunan Provincial Natural Science Foundation of China (No. 14JJ1012), and the construct program of the key discipline in Hunan province.
机构署名:
本校为其他机构
院系归属:
数学与统计学院
摘要:
Lawrence Zalcman's conjecture states that if is analytic and univalent in the unit disk , then for each , with equality only for the Koebe function and its rotations. This conjecture remains open although it has been verified for a few geometric subclasses of the class of univalent analytic functions. In this paper, we consider this problem for the family of normalized functions f analytic and univalent in the unit disk |z| < 1 satisfying the condition Functions satisfying this condition are known to be convex in some direction (and hence close-to-convex and univalent) in |z| < 1. A few other ...

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