A subclass of harmonic univalent mappings with a restricted analytic part
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 841-854
Published 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
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