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Author (up) Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O. doi  openurl
  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 (up) Arbelaez, H.; Bravo, V.; Hernandez, R.; Sierra, W.; Venegas, O. doi  openurl
  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;  
  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 (up) Bravo, V.; Hernandez, R.; Venegas, O. pdf  doi
openurl 
  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;  
  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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