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univalent Functions and Diff(S^1)/S^1

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Acta Mathematica Sinica,English Series 2012年第6期28卷 1233-1236页

作者： Simon DAVIS Research Foundation of Southern California

The relation between Diff（S^1）/S^1 and the space of univalent analytic functions on the disk is elucidated and shown to provide upper bounds for the volumes of exhaustive approximations to an analytic submanifold of an infinite-dimensional space. The maximum magnitudes of the coefficients in the series expansions of univalent superanalytic functions on the superdisk are inferred.

关键词： univalent diffeomorphism group superanalytic functions

NEW RESULTS FOR A CLASS OF univalent FUNCTIONS

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Acta Mathematica Scientia 2019年第6期39卷 1579-1588页

作者：彭志刚 Milutin OBRADOVIC Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and StatisticsHubei UniversityWuhan 430062China Department of Mathematics Faculty of Civil EngineeringUniversity of BelgradeBulevar Kralja Aleksandra 7311000Serbia

Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈C:|z|<1}, normalized by the conditions f(0) = 0 and f'(0) = 1. Let U denote the set of all functions f ∈ A satisfying the condition |(z/f(z))^2f'(z)-1|<1 for z∈D.Let Ω be the class of all f∈A for which |zf'(z)-f(z)|<1/2, z∈D.In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.

关键词： analytic univalent coefficient Hadamard product

Faber polynomials with applications to univalent functions with quasiconformal extensions

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Science China Mathematics 2009年第10期52卷 2121-2131页

作者： SHEN YuLiang Department of Mathematics, Soochow University, Suzhou 215006, China Department of Mathematics Soochow University Suzhou China

We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obt... 详细信息

关键词： univalent function quasiconformal mapping Faber polynomial Grunsky operator

univalent Criteria for Analytic Functions Involving Schwarzian Derivative

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Communications in Mathematical Research 2019年第4期35卷 359-366页

作者： HU ZHEN-YONG WANG QI-HAN HE LIANG-MIAO LONG BO-YONG Ji You-qing School of Mathematical Sciences Anhui University

In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence cr... 详细信息

关键词： analytic function univalent function Schwarzian derivative univalent criteria

Coefficient Estimates for a Class of m-fold Symmetric Bi-univalent Function Defined by Subordination

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Communications in Mathematical Research 2019年第1期35卷 57-64页

作者： Guo Dong Tang Huo Ao En Xiong Liang-peng Ji You-qing Foundation Department Chuzhou Vocational and Technical CollegeChuzhouAnhui239000 School of Mathematics and Statistics Chifeng UniversityChifengInner Mongolia024000 School of Mathematics and Statistics Wuhan UniversityWuhan430072 不详

In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.

关键词： analytic function univalent function coefficient estimate m-fold symmetric bi-univalent function subordination

Coefficient Estimates for Bi-univalent Bazilevic Functions

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Analysis in Theory and Applications 2014年第3期30卷 275-280页

作者： Nicoleta Ularu University of Pitesti Targul din Vale Str. No. 1 110040 Pitesti Arges Romania University "Ioan Slavici" from Timisoara Aurel Paunescu Podeanu Str.No. 144Timisoara Romania

In this paper we consider the class of Bazilevic functions for bi-univalent functions. For this we will estimate the coefficients a2 and a3 using Caratheodory func- tions and the method of differential subordination.

关键词： Analytic univalent unit disk bi-univalent Bazilevic functions.

Coefficient Estimates for a Certain General Subclass of Analytic and Bi-univalent Functions

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Applied Mathematics 2014年第7期5卷 1047-1052页

作者： Nanjundan Magesh Jagadeesan Yamini Department of Mathematics Govt First Grade College Bangalore India Post-Graduate and Research Department of Mathematics Government Arts College for Men Krishnagiri India

Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass of analytic and bi-univalent functions defined in the open unit disc U. Further, we find estimates on the coefficients and for functions in this subclass. Many relevant connections with known or new results are pointed out.

关键词： Analytic Functions univalent Functions Bi-univalent Functions Bi-Starlike Functions

Integral Means of univalent Solution for Fractional Differential Equation

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Applied Mathematics 2012年第6期3卷 590-593页

作者： Rabha W. Ibrahim Maslina Darus School of Mathematical Sciences Faculty of science and Technology University Kebangsaan Malaysia Bangi Malaysia

By employing the Srivastava-Owa fractional operators, we consider a class of fractional differential equation in the unit disk. The existence of the univalent solution is founded by using the Schauder fixed point theorem while the uniqueness is obtained by using the Banach fixed point theorem. Moreover, the integral mean of these solutions is studied by applying the concept of the subordination.

关键词： Fractional Calculus Subordination Superordination univalent Solution Fractional Differential Equation Integral Mean

PRECISE VALUES OF THE BLOCH CONSTANTS OF CERTAIN LOG-p-HARMONIC MAPPINGS

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Acta Mathematica Scientia 2021年第1期41卷 297-310页

作者：刘名生骆莉芳 School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

The aim of this article is twofold.One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method.The other is to obtain the precise values of Bloch constants for certain log-p-harmonic mappings.These results improve upon the corresponding results given in Bai et al.(Complex Anal.Oper.Theory,13(2):321-340,2019).

关键词： Bloch constant Landau theorem Bloch theorem biharmonic mappings polyharmonic mappings log-p-harmonic mappings univalent