THE FEKETE-SZEG ¨O PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

An analytic function f in the unit disk D := {z ∈ C : |z| < 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re ?eiδ(1-z)2f′(z)? > 0, z ∈ D. For the class C(k) of all close-to-convex functi...

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Bibliographic Details
Published in数学物理学报（英文版） no. 5; pp. 1571 - 1583
Main Authors Bogumila KOWALCZYK, Adam LECKO
Format Journal Article
LanguageEnglish
Published Chair of Complex Analysis, University of Warmia and Mazury, ul. S loneczna 54,10-710 Olsztyn, Poland 2014
Subjects
close-to-convex functions
close-to-convex functions with argumentδ
functions convex in the positive direction of the imaginary axis
close-to-convex functions with respect to the Koebe function
Fekete-Szeg¨o problem
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Summary:An analytic function f in the unit disk D := {z ∈ C : |z| < 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re ?eiδ(1-z)2f′(z)? > 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szeg¨o problem is studied.
ISSN:0252-9602