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Author 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 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 Arbelaez, H.; Hernandez, R.; Sierra, W.
Title Normal harmonic mappings Type
Year 2019 Publication Monatshefte Fur Mathematik Abbreviated Journal Mon.heft. Math.
Volume 190 Issue 3 Pages 425-439
Keywords Harmonic mappings; Normal family; Normal mappings; Univalent function
Abstract The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk D to the complex plane. In particular, we obtain necessary conditions for a function f to be normal.
Address [Arbelaez, Hugo] Univ Nacl Colombia, Medellin, Colombia, Email: hjarbela@unal.edu.co;
Corporate Author Thesis
Publisher Springer Wien Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0026-9255 ISBN Medium
Area Expedition Conference
Notes WOS:000490002700003 Approved
Call Number UAI @ eduardo.moreno @ Serial 1087
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Author Arbelaez, H.; Hernandez, R.; Sierra, W.
Title Lower and upper order of harmonic mappings Type
Year 2022 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.
Volume 507 Issue 2 Pages 125837
Keywords Harmonic mapping; Lower order; Upper order; Concave functions; Linearly connected domain; Schwarzian derivative
Abstract In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory. (C) 2021 Elsevier Inc. All rights reserved.
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 0022-247X ISBN Medium
Area Expedition Conference
Notes WOS:000775539700031 Approved
Call Number UAI @ alexi.delcanto @ Serial 1557
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