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Author (up) Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O.
Title Integral transforms for logharmonic mappings Type
Year 2021 Publication 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.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1029-242X ISBN Medium
Area Expedition Conference
Notes WOS:000626943300001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1354
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Author (up) Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O.
Title A new approach for the univalence of certain integral of harmonic mappings Type
Year 2020 Publication Indagationes Mathematicae-New Series Abbreviated Journal Indag. Math.-New Ser.
Volume 31 Issue 4 Pages 525-535
Keywords Univalent mappings; Integral transformation; Geometric function theory
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.
Address [Arbelaez, Hugo] Univ Nacl Colombia, Fac Ciencias, Sede Medellin, Medellin, Colombia, Email: hjarbela@unal.edu.co;
Corporate Author Thesis
Publisher Elsevier Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0019-3577 ISBN Medium
Area Expedition Conference
Notes WOS:000552682000001 Approved
Call Number UAI @ eduardo.moreno @ Serial 1211
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Author (up) Bravo, V.; Hernandez, R.; Venegas, O.
Title On the univalence of certain integral for harmonic mappings Type
Year 2017 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.
Volume 455 Issue 1 Pages 381-388
Keywords Harmonic mapping; Univalent functions; Integral transform
Abstract We generalize the problem of univalence of the integral of f'(z)(alpha) when f is univalent to the complex harmonic mappings. To do this, we extend the univalence criterion by Ahlfors in [1] to those mappings. (C) 2017 Elsevier Inc. All rights reserved.
Address [Bravo, Victor] Univ Valparaiso, Inst Matemat, Fac Ciencias, Valparaiso, Chile, Email: victor.bravo@uv.cl;
Corporate Author Thesis
Publisher Academic Press Inc Elsevier Science Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0022-247x ISBN Medium
Area Expedition Conference
Notes WOS:000424735900019 Approved
Call Number UAI @ eduardo.moreno @ Serial 826
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