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Author  |
Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O. |
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Title |
A new approach for the univalence of certain integral of harmonic mappings |
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Year |
2020 |
Publication |
Indagationes Mathematicae-New Series |
Abbreviated Journal |
Indag. Math.-New Ser. |
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Volume |
31 |
Issue |
4 |
Pages |
525-535 |
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Keywords |
Univalent mappings; Integral transformation; Geometric function theory |
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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. |
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Address |
[Arbelaez, Hugo] Univ Nacl Colombia, Fac Ciencias, Sede Medellin, Medellin, Colombia, Email: hjarbela@unal.edu.co; |
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Elsevier |
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English |
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0019-3577 |
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WOS:000552682000001 |
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Call Number |
UAI @ eduardo.moreno @ |
Serial |
1211 |
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Author |
Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O. |
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Title |
Integral transforms for logharmonic mappings |
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Year |
2021 |
Publication |
Journal of Inequalities and Applications |
Abbreviated Journal |
J. Inequal. Appl. |
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Volume |
2021 |
Issue |
1 |
Pages |
48 |
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Keywords |
Integral transform; Logharmonic mappings; Shear construction; Univalent mappings |
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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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1029-242X |
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WOS:000626943300001 |
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UAI @ alexi.delcanto @ |
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1354 |
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Author |
Arbelaez, H.; Hernandez, R.; Sierra, W. |
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Title |
Normal harmonic mappings |
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Year |
2019 |
Publication |
Monatshefte Fur Mathematik |
Abbreviated Journal |
Mon.heft. Math. |
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Volume |
190 |
Issue |
3 |
Pages |
425-439 |
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Keywords |
Harmonic mappings; Normal family; Normal mappings; Univalent function |
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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. |
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[Arbelaez, Hugo] Univ Nacl Colombia, Medellin, Colombia, Email: hjarbela@unal.edu.co; |
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Springer Wien |
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English |
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0026-9255 |
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WOS:000490002700003 |
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Call Number |
UAI @ eduardo.moreno @ |
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1087 |
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Author |
Arbelaez, H.; Hernandez, R.; Sierra, W. |
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Title |
Lower and upper order of harmonic mappings |
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Year |
2022 |
Publication |
Journal Of Mathematical Analysis And Applications |
Abbreviated Journal |
J. Math. Anal. Appl. |
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Volume |
507 |
Issue |
2 |
Pages |
125837 |
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Keywords |
Harmonic mapping; Lower order; Upper order; Concave functions; Linearly connected domain; Schwarzian derivative |
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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. |
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0022-247X |
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WOS:000775539700031 |
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UAI @ alexi.delcanto @ |
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1557 |
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