Research output: Contribution to journal › Article

Abstract

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 .

title = "Three Extremal Problems for Hyperbolically Convex Functions",

abstract = "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 .",

author = "Roger Barnard and Kent Pearce and George Williams",

year = "2004",

language = "English",

pages = "97--109",

journal = "Computational Methods and Function Theory",

Research output: Contribution to journal › Article

TY - JOUR

T1 - Three Extremal Problems for Hyperbolically Convex Functions

AU - Barnard, Roger

AU - Pearce, Kent

AU - Williams, George

PY - 2004

Y1 - 2004

N2 - 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 .

AB - 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 .