A new approach for the univalence of certain integral of harmonic mappings
Abstract
The principal goal of this paper is to extend the classical problem of find the values of α∈ for which the mappings, either Fα(z)=∫0z(f(ζ)/ζ)α dζ or fα(z)=∫0z(f'(ζ))α dζ are univalent, whenever f belongs to some subclasses of univalent mappings in , but in the case of harmonic mappings, considering the shear construction introduced by Clunie and Sheil-Small in CSS.
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