Hyperbolically convex functions and the generalized Fekete-Szegö functional

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)366-374
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Dec 15 2011


  • Fekete-Szegö functional
  • Hyperbolically convex functions
  • Julia variation


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