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The extreme points of a class of functions with positive real part
Published online by Cambridge University Press: 17 April 2009
Abstract
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Let P1 be the class of holomorphic functions on the unit disc U = {z: |z| < 1} for which f(0) = 1 and Re f > 0. Let also Pn be the corresponding class on the unit disc Un. The inequality |ak| ≤ 2 is known for the Taylor coefficients in the class P1. In this paper, it is generalised for the class Pn. If ρ = (ρ1, ρ2, …, ρn), with ρ1, ρ2, …, ρn nonegative integers whose greatest common divisor is equal to 1, we describe the form of the functions f ∈ Pn under the restriction |aρ| = 2. Under the same restriction, we give conditions for a function to be an extreme point of the class Pn.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 253 - 261
- Copyright
- Copyright © Australian Mathematical Society 1991
References
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