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

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 .

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 303; no. 2; pp. 661 - 668
Main Authors Choi, J.H., Kim, Y.C., Ponnusamy, S., Sugawa, T.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.03.2005
Elsevier
Subjects
Alexander transform
Convex of order α
Exact sciences and technology
Functions of a complex variable
Hypergeometric function
Mathematical analysis
Mathematics
Real functions
Sciences and techniques of general use
Special functions
Univalent function
Hypergeometric function
Alexander transform
Univalent function
Convex of order α
Alexander transformation
Mathematical analysis
Order alpha
Convex function
Convex of order a
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Summary: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 .
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.08.066