Univalent harmonic mappings convex in one direction

被引：12
|
作者：
Ponnusamy, S. [1 ]
Kaliraj, A. Sairam [2 ]
机构：
[1] Indian Stat Inst, Chennai Ctr, SETS, Madras 600113, Tamil Nadu, India
[2] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2014年 / 4卷 / 03期
关键词：
Univalent harmonic functions; Convex in one direction; Starlike in one direction; Close-to-convex; Fully starlike; Fully convex;
D O I：
10.1007/s13324-013-0066-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a criterion for a harmonic function to be convex in one direction. Also, we discuss the class of harmonic functions starlike in one direction in the unit disk D and obtain a method to construct univalent harmonic functions convex in one direction. Although the converse of classical Alexander's theorem for harmonic functions was proved to be false, we obtain a version of converse of it under a suitable additional condition.
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页码：221 / 236
页数：16
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