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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 Ferrada-Salas, A.; Hernandez, R.; Martin, M.J.
Title On Convex Combinations Of Convex Harmonic Mappings Type
Year 2017 Publication Bulletin Of The Australian Mathematical Society Abbreviated Journal Bull. Aust. Math. Soc.
Volume 96 Issue 2 Pages 256-262
Keywords convex harmonic mappings; convex combinations
Abstract The family F-lambda of orientation-preserving harmonic functions f = h + (g) over bar in the unit disc D (normalised in the standard way) satisfying h' (z) + g' (z) = 1/(1 + lambda z)(1 + (lambda) over barz), z is an element of D, for some lambda is an element of partial derivative D, along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in F-lambda are convex.
Address [Ferrada-Salas, Alvaro] Pontificia Univ Catolica Chile, Fac Matemat, Casilla 306, Santiago, Chile, Email: alferrada@mat.puc.cl;
Corporate Author Thesis
Publisher Cambridge Univ Press Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0004-9727 ISBN Medium
Area Expedition Conference
Notes WOS:000411403100010 Approved
Call Number UAI @ eduardo.moreno @ Serial 804
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Author Hernandez, R.; Martin, M.J.
Title Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings Type
Year 2015 Publication Journal Of Geometric Analysis Abbreviated Journal J. Geom. Anal.
Volume 25 Issue 1 Pages 64-91
Keywords Pre-Schwarzian derivative; Schwarzian derivative; Harmonic mappings; Univalence; Becker's criterion; Convexity
Abstract In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping f in the complex plane without assuming any additional condition on the (second complex) dilatation omega(f) of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove theorems analogous to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.
Address [Hernandez, Rodrigo] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Vina Del Mar, Chile, Email: rodrigo.hernandez@uai.cl;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1050-6926 ISBN Medium
Area Expedition Conference
Notes WOS:000348344200003 Approved
Call Number UAI @ eduardo.moreno @ Serial 452
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Author Hernandez, R.; Venegas, O.
Title Distortion Theorems Associated with Schwarzian Derivative for Harmonic Mappings Type
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;
Corporate Author Thesis
Publisher Springer Basel Ag Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1661-8254 ISBN Medium
Area Expedition Conference
Notes WOS:000469812800015 Approved
Call Number UAI @ eduardo.moreno @ Serial 1030
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