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Norm estimates for the Alexander transforms of convex functions of order alpha |
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| Authors: | JH Choi S Ponnusamy T Sugawa |
| Institution: | a Department of Mathematics Education, Daegu National University of Education, 1797-6 Daemyong 2 dong, Namgu, Daegu 705-715, South Korea b Department of Mathematics Education, Yeungnam University, 214-1 Daedong, Gyongsan 712-749, South Korea c Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India d Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan |
| 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. |
| Keywords: | Alexander transform Univalent function Convex of order α Hypergeometric function |
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