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Author Bravo, V.; Hernandez, R.; Ponnusamy, S.; Venegas, O.
Title Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings Type
Year 2022 Publication (down) 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.
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 0026-9255 ISBN Medium
Area Expedition Conference
Notes WOS:000750771000001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1531
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Author Bravo, V.; Hernandez, R.; Venegas, O.
Title On the univalence of certain integral for harmonic mappings Type
Year 2017 Publication (down) 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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Author Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O.
Title Integral transforms for logharmonic mappings Type
Year 2021 Publication (down) 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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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 Gaona, J.; Hernández, R.; Guevara, F.; Bravo, V.
Title Influence of a Function’s Coefficients and Feedback of the Mathematical Work When Reading a Graph in an Online Assessment System Type
Year 2022 Publication (down) International Journal of Emerging Technologies in Learning Abbreviated Journal Int. J. Emerg. Technol. Learn.
Volume 17 Issue 20 Pages 77-98
Keywords digital technology; distance education and online learning; mathematical activity; post-secondary education; task design
Abstract This paper shows the results of an experiment applied to 170

students from two Chilean universities who solve a task about reading a graph

of an affine function in an online assessment environment where the parameters

(coefficients of the graphed affine function) are randomly defined from an ad-hoc

algorithm, with automatic correction and automatic feedback. We distinguish two

versions: one of them with integer coefficients and the other one with decimal

coefficients in the affine function. We observed that the nature of the coefficients

impacts the mathematical work used by the students, where we again focus on

two of them: by direct estimation from the graph or by calculating the equation of

the line. On the other hand, feedback oriented towards the “estimation” strategy

influences the mathematical work used by the students, even though a non-negligible

group persists in the “calculating” strategy, which is partly explained by the

perception of each of the strategies.
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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 1863-0383 ISBN Medium
Area Expedition Conference
Notes Approved
Call Number UAI @ alexi.delcanto @ Serial 1654
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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 (down) 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 Bravo, V.; Hernandez, R.; Venegas, O.
Title Two-Point Distortion Theorems for Harmonic Mappings Type
Year 2023 Publication (down) 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.
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 0126-6705 ISBN Medium
Area Expedition Conference
Notes WOS:000969541800001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1789
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