THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

doi:10.1016/S0252-9602(14)60104-1

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1571-1583.doi: 10.1016/S0252-9602(14)60104-1

THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

Bogumi la KOWALCZYK|Adam LECKO*

Chair of Complex Analysis, University of Warmia and Mazury, ul. S loneczna 54, 10-710 Olsztyn, Poland

收稿日期:2013-02-07 出版日期:2014-09-20 发布日期:2014-09-20
通讯作者: Adam LECKO，alecko@matman.uwm.edu.pl E-mail:b.kowalczyk@matman.uwm.edu.pl; alecko@matman.uwm.edu.pl

THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

Bogumi la KOWALCZYK|Adam LECKO*

Chair of Complex Analysis, University of Warmia and Mazury, ul. S loneczna 54, 10-710 Olsztyn, Poland

Received:2013-02-07 Online:2014-09-20 Published:2014-09-20
Contact: Adam LECKO，alecko@matman.uwm.edu.pl E-mail:b.kowalczyk@matman.uwm.edu.pl; alecko@matman.uwm.edu.pl

摘要/Abstract

摘要：

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{e^iδ(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.

关键词: Fekete-Szeg¨o problem, close-to-convex functions, close-to-convex functions with respect to the Koebe function, close-to-convex functions with argument
, functions convex in the positive direction of the imaginary axis

Abstract:

Key words: Fekete-Szeg¨o problem, close-to-convex functions, close-to-convex functions with respect to the Koebe function, close-to-convex functions with argument

中图分类号:

30C45

Bogumi la KOWALCZYK, Adam LECKO. THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION[J]. 数学物理学报(英文版), 2014, 34(5): 1571-1583.

Bogumi la KOWALCZYK, Adam LECKO. THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION[J]. Acta mathematica scientia,Series B, 2014, 34(5): 1571-1583.

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THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

THE FEKETE-SZEGÖ|PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

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