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Author 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.  
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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 Bravo, V.; Hernandez, R.; Ponnusamy, S.; Venegas, O. doi  openurl
  Title Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings Type
  Year 2022 Publication Monatshefte Fur Mathematik Abbreviated Journal Monatsh. fur Math.  
  Volume Early Access Issue Pages  
  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 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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