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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

N. Samaris
N. Samaris
Affiliation:
Department of Mathematics, Faculty of Sciences, University of Patras, 26110 Patras, Greece
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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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