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The Growth Theorem for Strongly Starlike Mappings of Order α on Bounded Starlike Circular Domains
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作者 刘浩 李小申 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期28-33,共6页
The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if ... The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it. 展开更多
关键词 strongly starlike mappings of order α growth theorem startike circular domains
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The Growth Theorem for Almost Starlike Mappings of Order α on Bounded Starlike Circular Domains 被引量:3
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作者 冯淑霞 卢克平 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第2期50-56,共7页
In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it.... In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it. This type of domain on which we discuss is rather general,in the sense that the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. 展开更多
关键词 almost starlike mapping of order α growth theorem starlike circular domains
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THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER α ON THE UNIT POLYDISK IN C^n 被引量:14
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作者 刘小松 刘太顺 《Acta Mathematica Scientia》 SCIE CSCD 2012年第2期752-764,共13页
In this article, first, a sufficient condition for a starlike mapping of order a f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f ... In this article, first, a sufficient condition for a starlike mapping of order a f(x) defined on the unit ball in a complex Banach space is given. Second, the sharp estimate of the third homogeneous expansion for f is established as well, where f(z) = (f1(z), f2(z),..., fn(z))' is a starlike mapping of order a or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn, and D2fk(0)(z2) /2i= zk(∑l=1^b akzzl), k = 2t l=1 k = 1, 2,..., n. Our result states that the Bieberbaeh conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order α and biholomorphic starlike mappings) is partly proved. 展开更多
关键词 Estimate of the third homogeneous expansion starlike mapping of order a biholomorphic starlike mapping
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FEKETE AND SZEG INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER αON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN C^n 被引量:1
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作者 刘太顺 徐庆华 《Acta Mathematica Scientia》 SCIE CSCD 2017年第3期722-731,共10页
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 d... 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. 展开更多
关键词 Fekete-Szego problem starlike mappings of order α bounded starlike circulardomain
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A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α 被引量:21
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作者 LIU Xiao-song FENG Shu-xia 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第2期310-316,共7页
Suppose f is a spirallike function of type β and order α on the unit disk D.Let Ωn,p1,p2,…,pn={z=(z2,z2,…,zn)′∈C^n:∑j=1^n|zj)^Pj〈1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers.In this paper,we will pr... Suppose f is a spirallike function of type β and order α on the unit disk D.Let Ωn,p1,p2,…,pn={z=(z2,z2,…,zn)′∈C^n:∑j=1^n|zj)^Pj〈1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers.In this paper,we will prove that Φn,β2,γ2,…βn,γn(f)(z)=(f(z1), preserves spirallikeness of type β and order α on Ωn,p1,p2,…,Pn. 展开更多
关键词 K spirallike mapping of type β and order β starlike mapping of order α gener-alized Roper-Suffridge extension operator
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A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α 被引量:2
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作者 LIU Xiao-song FENG Shu-xia 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期22-28,共7页
Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn(f)(z)=(f(z1),(f(z1)/z1)^β2(f'(z1))^γ2 z2,…,(f(z1)/z1)^βn(f'(z... Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn(f)(z)=(f(z1),(f(z1)/z1)^β2(f'(z1))^γ2 z2,…,(f(z1)/z1)^βn(f'(z1))^γnzn)1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=(z1,z2,…,zn)'∈Cn:∑^n j=1|zj|^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers. 展开更多
关键词 almost starlike mapping of order α starlike mapping generalized Roper- Surffridge extension operator
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THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α
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作者 崔艳艳 王朝君 刘浩 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1454-1466,共13页
The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper. From the maximum modulus principle of holomorphic functions, we obtain that the generalized Roper-Suffridge o... The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper. From the maximum modulus principle of holomorphic functions, we obtain that the generalized Roper-Suffridge operators preserve strong and almost spirallike-hess of type β and order α on the unit ball B^n in C^n and on bounded and complete Reinhardt domains. Therefore we obtain that the generalized Roper-Suffridge operators preserve strong spirllikeness of type β, strong and almost starlikeness of order α, strong starlikeness on the corresponding domains.Thus we can construct more subclasses of spirallike mappings in several complex variables. 展开更多
关键词 strong and almost spirallike mappings of type β and order a Roper-Suffridgeoperators homogeneous expansion
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On Strongly Quasi-convex Mappings on Unit Ball in C^n
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作者 孔杰 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第2期104-110,共7页
Let B n be the unit ball in C n, we study strongly quasi_convex mappings and starlike mappings on B n. Several problems are discussed: (1) The relationship between strongly quasi_convex mappings and convex mappings... Let B n be the unit ball in C n, we study strongly quasi_convex mappings and starlike mappings on B n. Several problems are discussed: (1) The relationship between strongly quasi_convex mappings and convex mappings(starlike mappings); (2) The second order item coefficients for strongly quasi_convex mappings; (3) The strongly quasi_convex mappings on the unit polydisk. 展开更多
关键词 starlike mappings strongly quasi_convex mappings convex mappings
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The Study for Some Subclasses of Biholomorphic Mappings by an Unified Method
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作者 XU Qing-hua LIU Tai-shun 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期166-175,共10页
Let Ω∈ C^n be a bounded starlike circular domain with 0 ∈ Ω. In this paper, we introduce a class of holomorphic mappings Mg on Ω. Let f(z) be a normalized locally biholomorphic mapping on Ω such that Jf^-1 (z... Let Ω∈ C^n be a bounded starlike circular domain with 0 ∈ Ω. In this paper, we introduce a class of holomorphic mappings Mg on Ω. Let f(z) be a normalized locally biholomorphic mapping on Ω such that Jf^-1 (z) f(z) ∈Mg and z = 0 is the zero of order k+1 of f(z) - z. We obtain the growth and covering theorems for f(z). Especially, as corollaries, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown. 展开更多
关键词 growth and covering theorem starlike mapping subclasses of starlike mappings zero of order k 1
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ON THE SHARP GROWTH,COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n 被引量:2
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作者 刘小松 刘太顺 《Acta Mathematica Scientia》 SCIE CSCD 2007年第4期803-812,共10页
In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k + 1 of f(z) - z. The sharp growth, covering theorems for almos... In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k + 1 of f(z) - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings. 展开更多
关键词 Zero of order k 1 normalized biholomorphic mappings almost starlike mappings of order α starlike mappings of order α GROWTH covering theorems
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On the Fekete and Szego Problem for Starlike Mappings of Order α 被引量:3
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作者 Qing Hua XU Fang FANG Tai Shun LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2017年第4期554-564,共11页
Let Sα*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class Sα*, and then we generalize this result to the un... Let Sα*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class Sα*, and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in Cn. 展开更多
关键词 Fekete–Szego problem starlike mappings of order α sharp coefficient bound
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复Banach空间上推广的Roper-Suffridge延拓算子 被引量:2
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作者 崔艳艳 王朝君 《数学杂志》 CSCD 北大核心 2014年第3期515-520,共6页
本文研究了推广的Roper-Suffridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Suffridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert... 本文研究了推广的Roper-Suffridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Suffridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Suffridge算子的相应性质,推广了已有的结论. 展开更多
关键词 ROPER-SUFFRIDGE算子 ρ次抛物形β型螺形映照 强α次殆星形映照
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复Banach空间上推广的Roper-Suffridge算子的性质
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作者 崔艳艳 汪叶 《河南工程学院学报(自然科学版)》 2012年第3期70-72,共3页
讨论复Banach空间上两类推广的Roper-Suffridge算子,证明该算子保持强β型螺形映照、强α次殆星映形照、α次强β型螺形映照及α次殆β型螺形映照的性质,并作为特殊情况包含了已有的结论.
关键词 强β型螺形映照 α次强β型螺形映照 α次殆β型螺形映照 强α次殆星形映照
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THE GENERALIZED ROPER-SUFFRIDGE EXTENSION OPERATOR 被引量:29
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作者 冯淑霞 刘太顺 《Acta Mathematica Scientia》 SCIE CSCD 2008年第1期63-80,共18页
This note induces some generalized Roper-Suffridge extension operators such that they are used to construct some almost starlike mappings of order α and starlike mappings of order a on different domains.
关键词 Roper-Suffridge operator almost starlike mapping of order a starlike mappings of order
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ROPER-SUFFRIDGE EXTENSION OPERATOR ON A REINHARDT DOMAIN 被引量:2
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作者 李鸿军 冯淑霞 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1761-1774,共14页
Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =(z1, z′2,…, z′k)′∈ C × C^n2×…... Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =(z1, z′2,…, z′k)′∈ C × C^n2×…× Cnk: |z1|^2+ ||z2||2^p2+ … + ||zk ||k^pk〈 1} given〈1} give by F(z)=(f(z1)+f'(z1)∑j=2 kPj(zj,(f'(z1))1/p2 z2',…,(f'(z1))1/pkzk')', where f is a normaljized biholomorphic function k(z) =(f(z1) + f′(z1)=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj : C^nj→ C is a homogeneous polynomial of degree pj and zj =(zj1, …, zjnj)′∈ C^nj, nj ≥ 1, pj ≥ 1,||zj||j =(∑l=1 nj|zjl|^pj)1/pj. In this paper, some conditions for Pjare found under which the loperator p |zjl|pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively. 展开更多
关键词 Reinhardt domain Roper-Suffridge operator almost starlike of order α starlike mapping of order α strongly starlike mapping of order α
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On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables 被引量:1
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作者 Xiaosong LIU Taishun LIU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2021年第6期909-920,共12页
The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in C^(n) with a unified metho... The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in C^(n) with a unified method.Especially the results are sharp if the above mappings are further k-fold symmetric starlike mappings or k-fold symmetric starlike mappings of orderα.The obtained results unify and generalize the corresponding results in some prior literatures. 展开更多
关键词 Refined estimates of all homogeneous expansions starlike mapping starlike mapping of orderα k-fold symmetric Unified method
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Counterexamples Concerning Quasiconformal Extensions of Strongly Starlike Functions
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作者 Yu Liang SHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第10期1859-1868,共10页
M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin(απ/2) on the whole complex plane C which fixes the... M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin(απ/2) on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question. 展开更多
关键词 strongly starlike function quasiconformal extension Schwarzian derivative Teichmiiller mapping
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复Banach空间单位球上星形映射子族齐次展开式的精确估计
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作者 陈诗菲 刘小松 《岭南师范学院学报》 2018年第6期19-29,共11页
在复Banach空间单位球上建立了一类α次星形映射子族和一类α次殆星形映射子族第三、四项齐次展开式的精确估计,并且在一定的限制条件下,多复变数中关于星形映射子族第三、四项齐次展开式的猜想成立.
关键词 单位球 α次星形映射 α次殆星形映射 第三、四项齐次展开式
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A refinement about estimation of expansion coefficients for normalized biholomorphic mappings 被引量:20
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作者 LIU Taishun LIU Xiaosong 《Science China Mathematics》 SCIE 2005年第7期865-879,共15页
A refining estimation of homogeneous expansion for / is discussed, where f belongs to a subclass of all normalized biholomorphic mappings defined on the unit polydisk in Cn or the unit ball in complex Banach spaces, a... A refining estimation of homogeneous expansion for / is discussed, where f belongs to a subclass of all normalized biholomorphic mappings defined on the unit polydisk in Cn or the unit ball in complex Banach spaces, and x = 0 is a zero of order k+1 of f(x)-x. Moreover, an estimation of homogeneous expansion for subordinate mappings defined on the unit ball in complex Banach spaces is also given. 展开更多
关键词 de Branges theorem refining estimation of homogeneous expansion almost starlike mapping of order a starlike mapping of order a subordinate mapping.
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Sharp Growth Theorems and Coefficient Bounds for Starlike Mappings in Several Complex Variables 被引量:29
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作者 Hidetaka HAMADA Tatsuhiro HONDA 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2008年第4期353-368,共16页
Let B be the unit ball in a complex Banach space. Let S^*k+1(B) be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k + 1 of f(z) - z. The authors obtain sharp growth and cov... Let B be the unit ball in a complex Banach space. Let S^*k+1(B) be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k + 1 of f(z) - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^*k+1(B). 展开更多
关键词 Sharp coefficient bound Sharp covering theorem Sharp growth theorem starlike mapping Zero of order k
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