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ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS 被引量:14
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作者 彭志刚 韩秋秋 《Acta Mathematica Scientia》 SCIE CSCD 2014年第1期228-240,共13页
In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.
关键词 COEFFICIENT univalent function bi-univalent function SUBORDINATION
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On the Coefficients of Several Classes of Bi-univalent Functions Defined by Convolution 被引量:5
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作者 Guo Dong Li Zong-tao 《Communications in Mathematical Research》 CSCD 2018年第1期65-76,共12页
In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a... In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors. 展开更多
关键词 analytic and univalent functions coefficient bi-univalent function Hadamard product CONVOLUTION
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Second Hankel Determinants and Fekete-Szegö Inequalities for Some Sub-Classes of Bi-Univalent Functions with Respect to Symmetric and Conjugate Points Related to a Shell Shaped Region 被引量:2
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作者 Rayaprolu Bharavi Sharma Kalikota Rajya Laxmi 《Analysis in Theory and Applications》 CSCD 2018年第4期358-373,共16页
In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell... In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?. 展开更多
关键词 Analytic functions univalent functions Bi-univalent functions second Hankel determinants Fekete-Szeg?inequalities symmetric points conjugate points
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Fekete-Szegö Inequality for a Subclass of Bi-univalent Functions Associated with Hohlov Operator and Quasi-subordination 被引量:1
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作者 Guo Dong Tang Huo +1 位作者 Ao En Xiong Liang-peng 《Communications in Mathematical Research》 CSCD 2019年第3期235-246,共12页
In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclas... In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors. 展开更多
关键词 analytic function univalent function bi-univalent function coefficient estimate Fekete-Szegö inequality Hohlov operator quasi-subordination
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SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES 被引量:1
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作者 彭志刚 钟广祯 《Acta Mathematica Scientia》 SCIE CSCD 2017年第1期69-78,共10页
Let A be the space of functions analytic in the unit disk D = {z:|z| 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0 and|f'(z)(z/f(z))2-1|〈1(|z|〈1... Let A be the space of functions analytic in the unit disk D = {z:|z| 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0 and|f'(z)(z/f(z))2-1|〈1(|z|〈1).Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0and|zf'(z)-f(z)|〈1/2(|z|〈1).In this article,we discuss the properties of U and Ω. 展开更多
关键词 univalent function Starlike function Hadamard product extreme point sup-port point
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On Univalent Functions in Multiply Connected Domains
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作者 杨维奇 《Journal of Beijing Institute of Technology》 EI CAS 1994年第2期99-113,共15页
The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'... The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals. 展开更多
关键词 univalent functions integral representation variational methods/multiply connected domains parametric representation method extremal problem
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Coefficient Estimates for Certain Subclasses of Bi-Univalent Ma-Minda Mocanu-Convex Functions
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作者 C.Selvaraj O.S.Babu G.Murugusundaramoorthy 《Analysis in Theory and Applications》 2014年第2期141-150,共10页
In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Fu... In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several (known or new) consequences of the results are also pointed out. 展开更多
关键词 Analytic functions univalent functions bi-univalent functions bi-starlike functions bi-convex functions bi-Mocanu-convex functions SUBORDINATION Hohlov operator.
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Faber polynomials with applications to univalent functions with quasiconformal extensions 被引量:2
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作者 SHEN YuLiang Department of Mathematics, Soochow University, Suzhou 215006, China 《Science China Mathematics》 SCIE 2009年第10期2121-2131,共11页
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... 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 obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions. 展开更多
关键词 univalent function quasiconformal mapping Faber polynomial Grunsky operator 30C62 30C55 47B37
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Notes on Univalent Functions with Quasiconforml Extensions
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作者 Yu Liang SHEN Department of Mathematics,Suzhou University,Suzhou 215006,P.R.China E-mail:ylshen@suda.edu.cn 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第3期397-402,共6页
We make improvements to some of the constants concerned with univalent functions with quasiconformal extensions that have appeared in the literature.
关键词 univalent function Quasiconformal mapping Quasicircle
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ON UNIVALENT BLOCH FUNCTIONS
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作者 乌兰哈斯 《Acta Mathematica Scientia》 SCIE CSCD 2001年第1期37-40,共4页
A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommer... A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed. 展开更多
关键词 univalent Bloch functions essentially increasing functions Q(p) spaces
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Some Properties of Two Class of Analytic Functions Family 被引量:2
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作者 凌怡 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期96-100,共5页
Let A be the class of functions f(z)=z+sum from n=2 to ∞ (a_nZ^n) which are analytic in the unit disc, and let In this paper, Some properties of Q_α(β) and R_α(β) are investigated. In particular, Some results due... Let A be the class of functions f(z)=z+sum from n=2 to ∞ (a_nZ^n) which are analytic in the unit disc, and let In this paper, Some properties of Q_α(β) and R_α(β) are investigated. In particular, Some results due to chichra [4], Mocanu[5] and Obradovic[6] are extended. In addition, We also showed an error of S. Owa[8]. 展开更多
关键词 analytic function Hadamard product univalent function deviation theorem
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THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS 被引量:4
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作者 汤获 Erhan DENIZ 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1707-1719,共13页
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel function... In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z(Bκ+1^c f(z))′= κBκ^c f(z)-(κ- 1)Bκ+1^c f(z),where b, c, p ∈ C and κ = p +(b + 1)/2 ∈ C / Z0^-(Z0^-= {0,-1,-2, … }). The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out. 展开更多
关键词 differential subordination univalent functions Hadamard product admissible functions generalized Bessel functions
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DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS
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作者 Jacek DZIOK Ravinder Krishna RAINA Janusz SOKóL 《Acta Mathematica Scientia》 SCIE CSCD 2013年第3期609-620,共12页
This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z : |z|〈 1} satisfying the conditions that f(0) =0, f'(0)= 1, and α(1+zf''(z)/f'(... This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z : |z|〈 1} satisfying the conditions that f(0) =0, f'(0)= 1, and α(1+zf''(z)/f'(z)+(1-α)zf'(z)/f(z)∈p(U)for all z ∈ U, where αis a real number and p(z)=1+r^2z^2/1-Tz-T^2z^2(z∈ U). The number T = (1 -√5)/2 is such that T^2 = 1 + T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 (2011), 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory. 展开更多
关键词 univalent functions starlike functions SUBORDINATION Fibonacci numbers trisectrix of Maclaurin conchoid of de Sluze
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Some Results on Areally Mean Valent Functions
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作者 魏寒柏 李万社 张良 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第4期1-15, ,共15页
Let M be the class of areally mean univalent function, f ∈M and In this paper, we estimate the arithmetical mean of coefficients Dn(λ) and the arithmetical mean of successive coefficients tn(λ) =||Dn+1(λ)|-|Dn(λ)... Let M be the class of areally mean univalent function, f ∈M and In this paper, we estimate the arithmetical mean of coefficients Dn(λ) and the arithmetical mean of successive coefficients tn(λ) =||Dn+1(λ)|-|Dn(λ)||. Our results are sharp. In addition, we also generalize Hayman's theorem on integral mean 展开更多
关键词 areally mean univalent functions maximal growth integral mean
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New Results Subclasses of Analytic Functions Define by Opooladifferential Operator
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作者 Fatunsin L. M. Opoola T.O. 《Journal of Mathematics and System Science》 2017年第10期289-295,共7页
In this paper, using Opooladifferential operator, we introduce new subclasses of univalent functions andprovide δ -Neigbhourhoods properties, Inclusion relations for the subclasses of univalent functions.
关键词 univalent functions Normalised Identity function δ-Neigbhourhoods Inclusion relations Opoola differential operator.
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STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR
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作者 Samaneh Gholizadeh HAMIDI Suzeini Abdul HALIM Janusz SOKóL 《Acta Mathematica Scientia》 SCIE CSCD 2014年第5期1446-1460,共15页
In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk . For functions in this class Hαk (p,λ;h) we estimate the coefficients. Furthermore, some subordinatio... In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk . For functions in this class Hαk (p,λ;h) we estimate the coefficients. Furthermore, some subordination properties related to the operator Lαk are also derived. 展开更多
关键词 analytic functions univalent functions p-valent functions differential subor-dination Carlson-Shaffer operator Salagean operator Dziok-Srivastava oper-ator
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Weighted Integral Means of Mixed Areas and Lengths Under Holomorphic Mappings
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作者 Jie Xiao Wen Xu 《Analysis in Theory and Applications》 2014年第1期1-19,共19页
This note addresses monotonic growths and logarithmic convexities of the weighted ((1-t2)αdt2, -∞〈α〈∞, 0〈t〈1) integral means Aα,β( f ,·) and Lα,β( f ,·) of the mixed area (πr2)-βA( f... This note addresses monotonic growths and logarithmic convexities of the weighted ((1-t2)αdt2, -∞〈α〈∞, 0〈t〈1) integral means Aα,β( f ,·) and Lα,β( f ,·) of the mixed area (πr2)-βA( f ,r) and the mixed length (2πr)-βL( f ,r) (0≤β≤1 and 0〈r〈1) of f (rD) and?f (rD) under a holomorphic map f from the unit disk D into the finite complex plane C. 展开更多
关键词 Monotonic growth logarithmic convexity mean mixed area mean mixed length isoperimetric inequality holomorphic map univalent function.
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New Criterion for Starlike Integral Operators
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作者 Aabed Mohammed Maslina Darus Daniel Breaz 《Analysis in Theory and Applications》 2013年第1期21-26,共6页
In this paper, we introduce new sufficient conditions for certain integral operators to be starlike and p-valently starlike in the open unit disk.
关键词 Analytic function univalent function p-valently starlike integral operator.
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On a Generalized Integral Operator
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作者 Irina Dorca Daniel Breaz Mugur Acu 《Applied Mathematics》 2013年第11期1590-1594,共5页
We have considered several integral operators from literature and we have made a generalization of them. It can be easily seen that their properties are also preserved. Therefore, we use known results concerning the s... We have considered several integral operators from literature and we have made a generalization of them. It can be easily seen that their properties are also preserved. Therefore, we use known results concerning the starlike functions (see [1,2]) and we unify some known integral operators (see [3]) into one single integral operator, called I1(z), in Section 3 of this paper. 展开更多
关键词 univalent function Integral Operator GENERALIZATION Particular Cases
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Some Radius Problems Related to a Certain Subclass of Analytic Functions 被引量:2
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作者 Oh Sang KWON Young Jae SIM +1 位作者 Nak Eun CHO H.M.SRIVASTAVA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第7期1133-1144,共12页
For real parameters αand β such that 0≤α 〈 1 〈β, we denote by S(α,β) the class of normalized analytic functions which satisfy the following two-sided inequality:where U denotes the open unit disk. We find ... For real parameters αand β such that 0≤α 〈 1 〈β, we denote by S(α,β) the class of normalized analytic functions which satisfy the following two-sided inequality:where U denotes the open unit disk. We find a sufficient condition for functions to be in the class S(α,β) and solve several radius problems related to other well-known function classes. 展开更多
关键词 Analytic functions univalent functions starlike functions functions of bounded real pos-itive real part radius problems
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