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REMARKS ON THE UNIVALENCE CRITERION OF PASCU AND PASCU

Part of: Geometric function theory

Published online by Cambridge University Press:  22 August 2013

VAIDHYANATHAN BHARANEDHAR  and
SAMINATHAN PONNUSAMY
VAIDHYANATHAN BHARANEDHAR
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India email bharanedhar3@gmail.com
SAMINATHAN PONNUSAMY*
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
*
✉samy@isichennai.res.in,samy@iitm.ac.in
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Abstract

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We consider a recent work of Pascu and Pascu [‘Neighbourhoods of univalent functions’, Bull. Aust. Math. Soc. 83(2) (2011), 210–219] and rectify an error that appears in their work. In addition, we study certain analogous results for sense-preserving harmonic mappings in the unit disc $\vert z\vert \lt 1$. As a corollary to this result, we derive a coefficient condition for a sense-preserving harmonic mapping to be univalent in $\vert z\vert \lt 1$.

Keywords

analyticunivalentconvexclose-to-convex and harmonic mappings

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C50: Coefficient problems for univalent and multivalent functions 30C55: General theory of univalent and multivalent functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 210 - 216
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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