COEFFICIENT CONDITIONS FOR HARMONIC UNIVALENT MAPPINGS AND HYPERGEOMETRIC MAPPINGS

被引：19

作者：

Bharanedhar, S. V. ^{[1
]}

Ponnusamy, S. ^{[2
]}

机构：

[1] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India

[2] Indian Stat Inst, Chennai Ctr, SETS, Madras 600113, Tamil Nadu, India

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2014年 / 44卷 / 03期

关键词：

Harmonic; univalent; close-to-convex; starlike and convex mappings; coefficient estimates; Gaussian hypergeometric functions; Hadamard product (convolution);

D O I：

10.1216/RMJ-2014-44-3-753

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic close-to-convex (respectively, fully starlike) functions involving Gaussian hypergeometric functions. In addition, we present a convolution characterization for a class of univalent harmonic functions discussed recently by Mocanu, and later by Bshouty and Lyzzaik in 2010. Our approach provides examples of harmonic polynomials that are close-to-convex and starlike, respectively.

引用

页码：753 / 777

页数：25

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