Univalency of convolutions of harmonic mappings

被引：13

作者：

Boyd, Z. ^{[1
]}

Dorff, M. ^{[1
]}

Nowak, M. ^{[2
]}

Romney, M. ^{[3
]}

Woloszkiewicz, M. ^{[2
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Marie Curie Sklodowska Univ, Dept Math, PL-20031 Lublin, Poland

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 234卷

关键词：

Harmonic mappings; Convolutions; Univalence;

D O I：

10.1016/j.amc.2014.01.162

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping phi(z)=z/(1-z)with respective dilatations -xz and -yz, where vertical bar x vertical bar = vertical bar y vertical bar = 1. We prove that any such convolution is univalent. Furthermore, in the case that x = y = -1, we show the resulting convolution is convex. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：326 / 332

页数：7