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Author Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O.
Title Integral transforms for logharmonic mappings Type
Year 2021 Publication (up) Journal of Inequalities and Applications Abbreviated Journal J. Inequal. Appl.
Volume 2021 Issue 1 Pages 48
Keywords Integral transform; Logharmonic mappings; Shear construction; Univalent mappings
Abstract Bieberbach'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.
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ISSN 1029-242X ISBN Medium
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Notes WOS:000626943300001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1354
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