Remarks on the univalence criterion of Pascu and Pascu

Authors

  • V. Bharanedhar Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
  • S. Ponnusamy Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India.

Keywords:

analytic, univalent, convex, close-to-convex and harmonic mappings

Abstract

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 analogue results for sense-preserving harmonic mappings in the unit disk \(|z| < 1\). As a corollary to this result, we derive a coefficient condition for a sense-preserving harmonic mapping to be univalent in \(|z| < 1\). 10.1017/S0004972713000610

Author Biographies

V. Bharanedhar, Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India

Department of Mathematics, Ph.D scholar

S. Ponnusamy, Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India.

Professor and Head

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles
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