Hyperbolically convex functions and the generalized Fekete-Szegö functional

Roger W. Barnard; David Martin; G. Brock Williams

doi:10.1016/j.jmaa.2011.05.072

Hyperbolically convex functions and the generalized Fekete-Szegö functional

Roger W. Barnard, David Martin, G. Brock Williams

Mathematics and Statistics

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Abstract

We describe extremal functions for the generalized Fekete-Szegö functional |ta3+a22| over the class of hyperbolically convex functions. We apply the Julia variational formula to reduce the problem to mappings onto hyperbolic polygons having no more than two proper sides. In general, this is the best result possible. We show that both one-sided and two-sided maps can be extremal for different sub-classes.

Original language	English
Pages (from-to)	366-374
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	384
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.05.072
State	Published - Dec 15 2011

Keywords

Fekete-Szegö functional
Hyperbolically convex functions
Julia variation

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10.1016/j.jmaa.2011.05.072

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abstract = "We describe extremal functions for the generalized Fekete-Szeg{\"o} functional |ta3+a22| over the class of hyperbolically convex functions. We apply the Julia variational formula to reduce the problem to mappings onto hyperbolic polygons having no more than two proper sides. In general, this is the best result possible. We show that both one-sided and two-sided maps can be extremal for different sub-classes.",

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AB - We describe extremal functions for the generalized Fekete-Szegö functional |ta3+a22| over the class of hyperbolically convex functions. We apply the Julia variational formula to reduce the problem to mappings onto hyperbolic polygons having no more than two proper sides. In general, this is the best result possible. We show that both one-sided and two-sided maps can be extremal for different sub-classes.

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KW - Julia variation

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Hyperbolically convex functions and the generalized Fekete-Szegö functional

Abstract

Keywords

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