Some classes of harmonic mappings with analytic part defined by subordination

Authors: SHUHAI LI, Ma Li-na, AO EN, TANG HUO

Abstract: Let $S_{H}$ be the class of functions $f=h+\bar{g}$ that are harmonic univalent and sense-preserving in the open unit disk $\mathbb{U}=\{z\in \mathbb{C}:|z|<1\}$, where $h,$ $g$ are analytic and $f(0)=f_{z}'(0)-1=0$ in $ \mathbb{U}.$ In this paper, we investigate the properties of some subclasses of $S_{H}$ such that $h(z)$ is a starlike (or convex) function defined by subordination. We provide coefficient estimates, extremal function, distortion and growth estimates of $g$, growth, and Jacobian estimates of $f$. We also obtain area estimates and covering theorems of the classes. The results presented here generalize some known results.

Keywords: Harmonic univalent function, subordination, coefficient estimate, distortion, area estimate, covering theorem

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