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

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Arbelaez, Hugo
Bravo, Victor
Hernandez, Rodrigo
Sierra, Willy
Venegas, Osvaldo
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INDAGATIONES MATHEMATICAE-NEW SERIES,Vol.31,525-535,2020
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Abstract
The principal goal of this paper is to extend the classical problem of finding the values of alpha is an element of C for which either (f) over cap (alpha) (z) = integral(z)(0) (f (zeta)/zeta)(alpha) d zeta or f(alpha) (z) = integral(z)(0)(f' (zeta))(alpha)d zeta are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4]. (C) 2020 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
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