Communications of the
Korean Mathematical Society CKMS

In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $\mathcal{S}^{\delta}[\alpha]$, $0\leq \alpha < 1$, $-\infty < \delta < \infty$ which has been introduced and studied by Kumar \cite{Kumar87} (see also \cite{Mishra95}, \cite{MishraChoudhury95}, \cite{MishraDas96}, \cite{MishraGochhayat06}). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bound for the Bloch's constant for all functions in that family.

Keywords: harmonic univalent mapping, Bloch's constant, coefficient estimates, growth theorem, distortion theorem, covering theorem, area theorem

MSC numbers: Primary 30C45; Secondary 30C50, 30C55