Univalence criterion for harmonic mappings and Φ-like functions
Article Type
Research Article
Publication Title
Complex Variables and Elliptic Equations
Abstract
In this paper, we obtain a new characterization for univalent harmonic mappings and obtain a structural formula for the associated function which defines the analytic ф-like functions in the unit disk. The new criterion stated in this article for the injectivity of harmonic mappings implies the well-known results of Kas’yanyuk [10] and Brickman [3] for analytic functions, but with a simpler proof than theirs. A number of consequences of the characterization, and examples are also presented. Further investigation provides a new method to construct univalent harmonic mappings with the help of an improved distortion theorem.
First Page
1767
Last Page
1779
DOI
10.1080/17476933.2017.1409741
Publication Date
12-2-2018
Recommended Citation
Graf, Sergey Yu; Ponnusamy, Saminathan; and Starkov, Victor V., "Univalence criterion for harmonic mappings and Φ-like functions" (2018). Journal Articles. 1103.
https://digitalcommons.isical.ac.in/journal-articles/1103