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

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

Abstract:

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.

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

CLC Number:

30C45

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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