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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. | ||||
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Language | Summary Language | Original Title | |||
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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.; 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; | ||||
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Publisher | Elsevier | Place of Publication | Editor | ||
Language | English | Summary Language | Original Title | ||
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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.; Ponnusamy, S.; Venegas, O. | ||||
Title | Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings | Type | |||
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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Language | Summary Language | Original Title | |||
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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 | 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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Publisher | Academic Press Inc Elsevier Science | Place of Publication | Editor | ||
Language | English | Summary Language | Original Title | ||
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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 | 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 | 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 | |||
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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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