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arXiv · 1909.05633

A new approach for the univalence of certain integral of harmonic mappings

Hugo Arbeláez·Víctor Bravo·Rodrigo Hernández·Willy Sierra·Osvaldo Venegas
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Abstract

The principal goal of this paper is to extend the classical problem of find the values of $\alpha\in \C$ for which the mappings, either $F_\alpha(z)=\int_0^z(f(\zeta)/\zeta)^\alpha d\zeta$ or $f_\alpha(z)=\int_0^z(f'(\zeta))^\alpha d\zeta$ are univalent, whenever $f$ belongs to some subclasses of univalent mappings in $\D$, but in the case of harmonic mappings, considering the \textit{shear construction} introduced by Clunie and Sheil-Small in \cite{CSS}.

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Hugo Arbeláez, Víctor Bravo, Rodrigo Hernández, Willy Sierra, Osvaldo Venegas. 2019-09-12. A new approach for the univalence of certain integral of harmonic mappings. https://arxiv.org/abs/1909.05633

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