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Frontiers of Mathematics in China 2016年第6期11卷 1471-1500页

作者： Nak Eun CHO Bogumila KOWALCZYK Adam LECKO Department of Applied Mathematics Pukyong National University Busan 608-737 Korea Department of Complex Analysis University of Warmia and Mazury ul. S}oneczna 54 10-710 Olsztyn Poland

Given α∈[0, 1], let hα（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{e^iδ zf′（z）/hα（z）} 〉 0, z ∈ D. For the class l（hα） of all close-to-convex functions with respect to hα, the fekete-szego problem is studied.

关键词： fekete-szego problem close-to-convex functions close-to-convex functions with argument δ close-to-convex functions with respect to a convex function functions of bounded turning

fekete and szego problem for a subclass of quasi-convex mappings in several complex variables

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Frontiers of Mathematics in China 2015年第6期10卷 1461-1472页

作者： Qinghua XU Ting YANG Taishun LIU Huiming XU College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 China Department of Mathematics Huzhou University Huzhou 313000 China College of Mathematics Physics and Information Engineering Zhejiang Normal UniversityJinhua 321004 China

Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that maxf∈A ｜a3 - λa22｜ ≤ max{1/3, ｜λ - 1}, ,λ ∈ C, and the estimate is sharp for each ∈. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

关键词： fekete-szego problem quasi-convex mappings of type A quasi-convex mappings of type B quasi-convex mappings of type C

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variables

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Chinese Annals of Mathematics,Series B 2020年第1期41卷 37-48页

作者： Qinghua XU Taishun LIU Xiaosong LIU School of Science Zhejiang University of Science and TechnologyHangzhou 310023China Department of Mathematics Huzhou Teacher’s UniversityHuzhou 313000ZhejiangChina School of Mathematics and Computation Science Lingnan Normal UniversityZhanjiang 524048GuangdongChina

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C^n,which are natural extensions to higher dimensions of som... 详细信息

关键词： Coefficient inequality fekete-szego problem Quasi-convex mappings

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THE fekete-SZEG problem FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

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Acta Mathematica Scientia 2014年第5期34卷 1571-1583页

作者： Bogumila KOWALCZYK Adam LECKO Chair of Complex Analysis University of Warmia and Mazury ul. S loneczna 5410710 Olsztyn Poland

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-szego problem is studied.

关键词： fekete-szego problem close-to-convex functions close-to-convex functionswith respect to the Koebe function close-to-convex functions with argumentδ functions convex in the positive direction of the imaginary axis

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Journal of Mathematical Research with Applications 2021年第6期41卷 579-593页

作者： En AO Shuhai LI Huo TANG Collage of Mathematics and Computer Science Chifeng University

In this paper we introduce and investigate a new generalized class of bi-univalent functions defined by using(s, t)-derivative operator and quasi-subordination. We obtain the estimates of the first two coefficients |a|, |a| and general coefficient |a|(n ≥ 4) by using Faber polynomial expansion for the new class and some of its subclasses. And then we solve fekete-Szeg? probelm for the newly defined classes.

关键词： bi-univalent function $\left( {s,t} \right)$-derivative quasi-subordination coefficient estimate fekete-szego problem Faber polynomial expansion

fekete AND SZEG INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER αON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN C^n

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Acta Mathematica Scientia 2017年第3期37卷 722-731页

作者：刘太顺徐庆华 Department of Mathematics Huzhou University Huzhou 313000 China School of Science Zhejiang University of Science and Technology Hangzhou 310023 China

In this article, first, we establish the fekete and szego inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

关键词： fekete-szego problem starlike mappings of order α bounded starlike circulardomain

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A Certain Subclass of Analytic Functions with Bounded Positive Real Part

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Advances in Pure Mathematics 2013年第4期3卷 409-414页

作者： Young Jae Sim Oh Sang Kwon Department of Mathematics Kyungsung UniversityBusanSouth Korea

For real numbers α and β such that 0≤α<1<β, we denote by T(α,β) the class of normalized analytic functions which satisfy , where U denotes the open unit disk. We find some relationships involving functions in t... 详细信息

For real numbers α and β such that 0≤αfekete-szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or bi-univalent functions.

关键词： Functions of Bounded Positive Real Part fekete-szego problem Inverse Functions Bi-Univalent Functions