Work

On univalent log-harmonic mappings

Year: 2019

Type: preprint

Abstract: We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general idea, for example, to construct log-harmonic Koebe mapping, log-harmonic right half-plane mapping and log-harmonic two-slits mapping 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 subclass of log-harmonic mappings are studied. Finally, we propose two conjectures, namely, log-harmonic coefficient and log-harmonic covering conjectures.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1905.10551

Authors: Liu, ZhiHong, Ponnusamy, Saminathan

Institutions: Guilin University of Technology, Indian Institute of Technology Madras

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Guilin University of Technology

Award: G66914283

OpenAlex ID: W2945322820

Cites: 7

Cited by: 3

Related to: 10