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 .
|Journal||Computational Methods and Function Theory|
|State||Published - 2004|