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

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