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Three Extremal Problems for Hyperbolically Convex Functions

Three Extremal Problems for Hyperbolically Convex Functions In this paper we apply a variational method to three extremal problems for hyperbolically convex functions posed by Ma and Minda and Pommerenke [6, 14]. We first consider the problem of extremizing Re f(z)/z. We determine the minimal value and give a new proof of the maximal value previously determined by Ma and Minda. We also describe the geometry of the hyperbolically convex functions $f(z)=\alpha z+a_{2}z^{2}+ a_{3}z^{3}+\cdots$ which maximize Rea 3. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Three Extremal Problems for Hyperbolically Convex Functions

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Publisher
Springer Journals
Copyright
Copyright © 2004 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321058
Publisher site
See Article on Publisher Site

Abstract

In this paper we apply a variational method to three extremal problems for hyperbolically convex functions posed by Ma and Minda and Pommerenke [6, 14]. We first consider the problem of extremizing Re f(z)/z. We determine the minimal value and give a new proof of the maximal value previously determined by Ma and Minda. We also describe the geometry of the hyperbolically convex functions $f(z)=\alpha z+a_{2}z^{2}+ a_{3}z^{3}+\cdots$ which maximize Rea 3.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References