Integral transforms for logharmonic mappings

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datacite.alternateIdentifier.citationJOURNAL OF INEQUALITIES AND APPLICATIONS,Vol.2021,,2021
datacite.alternateIdentifier.doi10.1186/s13660-021-02578-y
datacite.creatorArbelaez, Hugo
datacite.creatorBravo, Victor
datacite.creatorHernandez, Rodrigo
datacite.creatorSierra, Willy
datacite.creatorVenegas, Osvaldo
datacite.date2021
datacite.subject.englishIntegral transform
datacite.subject.englishLogharmonic mappings
datacite.subject.englishShear construction
datacite.subject.englishUnivalent mappings
datacite.titleIntegral transforms for logharmonic mappings
dc.date.accessioned2021-04-30T16:59:15Z
dc.date.available2021-04-30T16:59:15Z
dc.description.abstractBieberbach's conjecture was very important in the development of geometric function theory, not only because of the result itself, but also due to the large amount of methods that have been developed in search of its proof. It is in this context that the integral transformations of the type f(alpha)(z) = integral(z)(0)(f(zeta)/zeta)(alpha)d zeta or F-alpha(z) = integral(z)(0)(f '(zeta))(alpha)d zeta appear. In this note we extend the classical problem of finding the values of alpha is an element of C for which either f(alpha) or F-alpha are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of logharmonic mappings by considering the extension of the shear construction introduced by Clunie and Sheil-Small in (Clunie and Sheil-Small in Ann. Acad. Sci. Fenn., Ser. A I 9:3-25, 1984) to this new scenario.
dc.identifier.urihttp://repositoriodigital.uct.cl/handle/10925/3780
dc.language.isoen
dc.publisherSPRINGER
dc.sourceJOURNAL OF INEQUALITIES AND APPLICATIONS
oaire.resourceTypeArticle
uct.catalogadorWOS
uct.indizacionSCI
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