Norm estimates for the Alexander transforms of convex functions of order alpha

J. H. Choi, Y. C. Kim, S. Ponnusamy, T. Sugawa

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

The hyperbolic sup norm of the pre-Schwarzian derivative of a locally univalent function on the unit disk measures the deviation of the function from similarities. We present sharp norm estimates for the Alexander transforms of convex functions of order α, 0 ≤ α < 1.

Original languageEnglish
Pages (from-to)661-668
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume303
Issue number2
DOIs
Publication statusPublished - 2005 Mar 15
Externally publishedYes

Keywords

  • Alexander transform
  • Convex of order α
  • Hypergeometric function
  • Univalent function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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