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 A subclass of harmonic univalent mappings with a restricted analytic part Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 841-854 https://doi.org/10.4134/CKMS.c180272Published online July 31, 2019 Bikash Kumar Chinhara, Priyabrat Gochhayat, Sudhananda Maharana Sambalpur University; Sambalpur University; Indian Institute of Technology Indore Abstract : 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 Downloads: Full-text PDF   Full-text HTML