On univalent log-harmonic mappings-Reference-Cited by-同舟云学术

On univalent log-harmonic mappings

Published:2022 Issue:12 Volume:36 Page:4211-4224
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Liu Zhihong¹,Ponnusamy Saminathan²

Affiliation:

1. College of Science, Guilin University of Technology, Guilin, Guangxi, People‘s Republic of China

2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India + Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

Abstract

We consider the class of univalent log-harmonic mappings on the unit disk. Firstly, we present general idea of constructing log-harmonic Koebe mappings, log-harmonic right half-plane mappings and log-harmonic two-slits mappings and then we show precise ranges of these mappings. Moreover, coefficient estimates for univalent log-harmonic starlike mappings are obtained. Growth and distortion theorems for certain special subclasses of log-harmonic mappings are studied. Finally, we propose two conjectures, namely, log-harmonic coefficient and log-harmonic covering conjectures.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference16 articles.

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3. Z. Abdulhadi, R. M. Ali, On rotationally starlike logharmonic mappings, Math. Nachr. 288 (2015) 723-729.

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5. Z. Abdulhadi, W. Hengartner, Spirallike logharmonic mappings, Complex Variables Theory Appl. 9 (1987) 121-130.

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