| Records |
| Author |
Hernandez, R.; Venegas, O. |
| Title |
Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings |
Type |
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| Year |
2019 |
Publication |
Complex Analysis And Operator Theory |
Abbreviated Journal |
Complex Anal. Oper. Theory |
| Volume |
13 |
Issue |
4 |
Pages  |
1783-1793 |
| Keywords |
Schwarzian derivative; Harmonic mappings; Distortion theorems |
| Abstract |
Let f be a complex-valued harmonic mapping defined in the unit disc D. The theorems of Chuaqui and Osgood (J Lond Math Soc 2:289-298, 1993), which assert that the bounds of the size of the hyperbolic norm of the Schwarzian derivative for an analytic function f imply certain bounds for distortion and growth of f, are extended to the harmonic case. |
| Address |
[Hernandez, Rodrigo] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Av Padre Hurtado 750, Vina Del Mar, Chile, Email: rodrigo.hernandez@uai.cl; |
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Thesis |
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| Publisher |
Springer Basel Ag |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
1661-8254 |
ISBN |
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Expedition |
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Conference |
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| Notes |
WOS:000469812800015 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
1030 |
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| Author |
Efraimidis, I.; Gaona, J.; Hernandez, R.; Venegas, O. |
| Title |
On harmonic Bloch-type mappings |
Type |
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| Year |
2017 |
Publication |
Complex Variables And Elliptic Equations |
Abbreviated Journal |
Complex Var. Elliptic Equ. |
| Volume |
62 |
Issue |
8 |
Pages |
1081-1092 |
| Keywords |
Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30 |
| Abstract |
Let f be a complex-valued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent. |
| Address |
[Efraimidis, I.] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain, Email: iason.efraimidis@uam.es |
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Thesis |
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| Publisher |
Taylor & Francis Ltd |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Series Issue |
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Edition |
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| ISSN |
1747-6933 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000399938900004 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
729 |
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| Author |
Bravo, V.; Hernandez, R.; Ponnusamy, S.; Venegas, O. |
| Title |
Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings |
Type |
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| Year |
2022 |
Publication |
Monatshefte Fur Mathematik |
Abbreviated Journal |
Monatsh. fur Math. |
| Volume |
199 |
Issue |
4 |
Pages |
733-754 |
| Keywords |
Pre-Schwarzian and Schwarzian derivatives; Harmonic and logharmonic mappings; Univalence criterion |
| Abstract |
We introduce definitions of pre-Schwarzian and Schwarzian derivatives for logharmonic mappings, and basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic. |
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Series Issue |
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Edition |
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| ISSN |
0026-9255 |
ISBN |
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Conference |
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| Notes |
WOS:000750771000001 |
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| Call Number |
UAI @ alexi.delcanto @ |
Serial |
1531 |
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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 |
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| 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; |
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Thesis |
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| Publisher |
Elsevier |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0019-3577 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000552682000001 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
1211 |
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| Author |
Bravo, V.; Hernandez, R.; Venegas, O. |
| Title |
On the univalence of certain integral for harmonic mappings |
Type |
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| 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; |
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Thesis |
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| Publisher |
Academic Press Inc Elsevier Science |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0022-247x |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000424735900019 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
826 |
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| Author |
Bravo, V.; Hernandez, R.; Venegas, O. |
| Title |
Two-Point Distortion Theorems for Harmonic Mappings |
Type |
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| Year |
2023 |
Publication |
Bulletin of the Malaysian Mathematical Sciences Society |
Abbreviated Journal |
Bull. Malaysian Math. Sci. |
| Volume |
46 |
Issue |
3 |
Pages |
100 |
| Keywords |
Two-point distortion; Harmonic mappings; Univalence criterion |
| Abstract |
We establish two-point distortion theorems for sense-preserving planar harmonic map -pings f = h + g in the unit disk D which satisfy harmonic versions of the univalence criteria due to Becker and Nehari. In addition, we also find two-point distortion theo-rems for the cases when h is a normalized convex function and, more generally, when h(D) is a c-linearly connected domain. |
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Series Issue |
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Edition |
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| ISSN |
0126-6705 |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000969541800001 |
Approved |
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| Call Number |
UAI @ alexi.delcanto @ |
Serial |
1789 |
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| Author |
Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O. |
| Title |
Integral transforms for logharmonic mappings |
Type |
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| 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. |
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Original Title |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
1029-242X |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000626943300001 |
Approved |
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| Call Number |
UAI @ alexi.delcanto @ |
Serial |
1354 |
| Permanent link to this record |
