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

2019/09/12 by Hugo Arbeláez, Arbeláez, Hugo, Víctor Bravo +7
Mathematics · #44A20 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30C45 #Secondary: 30C55

paper · pdf · doi:10.48550/arxiv.1909.05633

openalex publication_date 2019/09/12 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

The principal goal of this paper is to extend the classical problem of find\nthe values of \α\∈ C for which the mappings, either\nF_\α(z)=\∫₀^z(f(\ζ)/\ζ)^\α d\ζ or\nf_\α(z)=\∫₀^z(f'(\ζ))^\α d\ζ are univalent, whenever f\nbelongs to some subclasses of univalent mappings in D, but in the case of\nharmonic mappings, considering the \shear construction introduced by\nClunie and Sheil-Small in citeCSS.\n

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