Three Extremal Problems for Hyperbolically Convex Functions

Roger Barnard, Kent Pearce, George Williams

Research output: Contribution to journalArticlepeer-review


In this paper we apply a variational method to three extremal problems for hyperbolically convex functions posed by Ma and Minda and Pommerenke. 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)=α z + a2 z2 + a3 z3 + . . . which maximize Re a3 .
Original languageEnglish
Pages (from-to)97-109
JournalComputational Methods and Function Theory
StatePublished - 2004


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