Convolution properties of the harmonic Koebe function and its connection with 2-starlike mappings

被引：8

作者：

Nagpal, Sumit ^{[1
]}

Ravichandran, V. ^{[1
]}

机构：

[1] Univ Delhi, Dept Math, Delhi 110007, India

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2015年 / 60卷 / 02期

关键词：

Salagean operator; close-to-convex; univalent harmonic mappings; starlike; convex; sense-preserving; convolution; convex in one direction; UNIVALENT-FUNCTIONS; CONVEX-FUNCTIONS; HYPERGEOMETRIC-FUNCTIONS; STARLIKE;

D O I：

10.1080/17476933.2014.907284

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1984, Clunie and Sheil-Small constructed the harmonic Koebe function expecting it to play the role of extremal function for extremal problems over the class of sense-preserving harmonic univalent functions suitably normalized in the open unit disc. In this paper, we investigate the convolution properties of . In addition, we discuss the geometric properties of -starlike functions defined using the Salagean differential operator. Given a -starlike function , the product is shown to be univalent and convex in the direction of the real axis.

引用

页码：191 / 210

页数：20

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