# Growth and Distortion Theorems for Some Univalent Harmonic Mappings

## Authors

Deepali Khurana
Department of Mathematics, Hans Raj Mahila Maha Vidyalya, Jalandhar-144001, Punjab, India
Raj Kumar
Department of Mathematics, DAV University, Jalandhar-144001, Punjab, India
Sushma Gupta
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, Punjab, India
Sukhjit Singh
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, Punjab, India

### Synopsis

Let $$S$$ and $$K$$ denote the usual classes of normalized univalent analytic and normalized convex analytic functions, respectively. Similarly, let $$S_{H}^{0}$$ and $$K_{H}^{0}$$, respectively, denote these classes in the harmonic case. It is known that the classes $$S_{H}^{o}(S)=\{h+\overline{g} \in S_{H}^{o}: \;\ h+e^{i\theta}g \in S\; {\rm for\; some} \; \theta \in \mathbb{R}\}$$ and $$K_{H}^{0}(K)=\{h+\overline{g}\in K_{H}^{0}: \; h+e^{i\theta}g\in K \;\ {\rm for\;\ some} \;\ \theta\in \mathbb{R}\}$$ are, respectively, subclasses of normalized univalent harmonic and normalized convex harmonic functions. We give estimates of some functionals defined on the functions of these classes.

Published
August 8, 2020
Series
Online ISSN
2582-3922