<bold>Fekete-Szegö</bold> <bold>problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter</bold>

doi:10.1007/s11464-015-0510-y

Front. Math. China

2016, Vol. 11

Issue (6) : 1471-1500 https://doi.org/10.1007/s11464-015-0510-y

RESEARCH ARTICLE

Fekete-Szegö problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter

Nak Eun CHO¹,Bogumiła KOWALCZYK²,Adam LECKO²(

)

¹. Department of Applied Mathematics, Pukyong National University, Busan 608-737, Korea
². Department of Complex Analysis, University of Warmia and Mazury, ul. Słoneczna 54, 10-710 Olsztyn, Poland

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Abstract

Given α ∈[0, 1], let h_α(z) := z/(1 − αz), z ∈ D := {z ∈ C: |z| <1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (−π/2, π/2) such that Re{eⁱ^δzf′(z)/h_α(z)} >0, z ∈ D. For the class C(h_α) of all close-to-convex functions with respect to h_α, the Fekete-Szegö problem is studied.

Keywords Fekete-Szegö problem close-to-convex functions close-to-convex functions with argumentδ close-to-convex functions with respect to a convex function functions of bounded turning

Corresponding Author(s): Adam LECKO

Issue Date: 18 October 2016

Cite this article:

Nak Eun CHO,Bogumiła KOWALCZYK,Adam LECKO. Fekete-Szegö problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter[J]. Front. Math. China, 2016, 11(6): 1471-1500.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0510-y
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I6/1471

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