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• W1915224241 abstract "Let $L_H$ denote the set of all normalized locally one-to-one and sense-preserving harmonic functions in the unit disc $Delta$. It is well-known that every complex-valued harmonic function in the unit disc $Delta$ can be uniquely represented as $f = h + overline{g}$, where $h$ and $g$ are analytic in $Delta$. In particular the decomposition formula holds true for functions of the class $L_H$. For a fixed analytic function $h$, an interesting problem arises - to describe all functions $g$, such that $f$ belongs to $L_H$. The case when $fin L_H$ and $h$ is the identity mapping was considered [2]. More general results are given in [3], where $fin L_H$ and letting $h$ to be a convex analytic mapping. The focus of our present research is to characterize the set of all functions $fin L_H$ having starlike analytic part $h$. In this paper, we provide coefficient, distortion and growth estimates of $g$. We also give growth and Jacobian estimates of $f$." @default.
• W1915224241 created "2016-06-24" @default.
• W1915224241 creator A5009846043 @default.
• W1915224241 creator A5062439594 @default.
• W1915224241 date "2014-04-07" @default.
• W1915224241 modified "2023-09-27" @default.
• W1915224241 title "Locally one-to-one harmonic functions with starlike analytic part" @default.
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