α次殆β型螺形映照齐次展开式的精细估计

从Loewner链的角度讨论C~n中单位球B~n上α次殆β型螺形映照齐次展开式的相关项的上界,并作为特殊情况得出β型螺形映照、星形映照和α次殆星形映照齐次展开式的相关项的上界估计,推广了螺形映照及星形映照齐次展开式的二次项系数的上界估计.     

ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n

In this article.a normalized biholomorphic mapping f defined on bounded starlike circular domain in C″is considered,where z=0 is a zero of order k 1 of f(z)(?) The sharp growth.covering theorems for almost starlike mappings of order a and starlile mappings of order wave established.Meanwhile,the construction of the above mappings on bounded starlike circular domain in C~n is also discussed,it provides the extremal mappings for the growth,covering theorems of the above mappings.     

The estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation in several complex variables

In this paper, we obtain the estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation on the unit ball of complex Banach spaces.Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in C~n. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.     

On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables

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 Cn 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 order α. The obtained results unify and generalize the corresponding results in some prior literatures.     

多复变数的抛物星形映射

本文给出了抛物星形映射,ρ次的抛物星形映射,抛物形β型螺形映射和ρ次的抛物形β型螺形映射的定义.证明了推广的Rope-Suffridge算子保持这些映射的几何性质不变.     

Cn中拟凸映射和星形映射的系数问题

§ 1.　Introduction　　Theconvexfunctionshavebeenextensivelystudiedinonecomplexvariable .Thesefunc tionsareeasilycharacterizedbysimpleanalyticorgeometricconditionsandtherearemanywellknownresultswhichcanhelpusunderstandtheirnature.However,thedifficultiesariseinsev eralcomplexvariables.Imposingtheconditionthatamappingbeconvexmappingturnsouttobeveryrestrictiveandsothefamilyofquasi convexmappingswasintroducedbyROPERKAandSUFFRIDGETJin [1 ].In [2 ]wehaveshown :thefamilyofquasi convexmappings…     

$\mathbb{C}^n$中单位球上$\rho$次抛物星形映射的一些估计

主要研究了$\mathbb{C}^n$中单位球$B^{n}$上$\rho \ (\rho \in [0,1))$次抛物星形映射的一些几何性质, 给出了该映射类的增长定理和掩盖定理, 及其齐次展开式中二次项的一些估计.     

ROPER-SUFFRIDGE EXTENSION OPERATOR ON A REINHARDT DOMAIN

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 × Cn2×···× Cnk: |z1|2+ ||z2||p22+ ··· + ||zk ||pk k 1} given11 by F P′j(zj),(f(z1))p2 z′2, ···,(f′(z1))pk z′k)′, 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 : Cnj-→ C is a homogeneous polynomial of degree pj and zj =(zj1, ···, zjnj)′∈ Cnj, nj ≥ 1, pj ≥ 1,nj1||zj ||j =()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.     

On set-valued mappings with starlike graphs

The paper studies some topological properties of starlike bodies. It is proved that the boundary of a starlike body is a Lipschitz surface. A separability theorem for starlike bodies is proved. It is shown that under some additional assumptions the starlike property of the graph provides the local Lipschitz property of the set-valued mapping itself. It is shown that F. Clark’s contingent and tangential cones are Boltyansky tents. On the base of these results, some lower and upper differentials for set-valued mappings with starlike graphs are constructed. Some theorems on fixed points of set-valued mappings with starlike values are proved.     

α次的殆星映射的充分判别条件

该文通过在cⁿ中的有界星形圆型域和复Banach空间中的单位球上建立一些偏微分不等式, 分别给出α 次的殆星映射在这两类域上的充分判别条件.     

一类α次殆星形映照的偏差定理

近年来,双全纯凸(准凸)映照的偏差定理的研究已经获得一些可喜成果,但目前星形映照的偏差定理研究成果还较少.利用α次殆星形映射的增长估计,我们得到了C~n中开单位球B~n上一类α次殆星形映射的偏差估计.对复Banach空间单位球B和Reinhard域Ω_p1,…,p_n,可得到同样的结论,正如猜想的一样.     

On some classes of bounded univalent mappings in several complex variables

Let B ⁿ be the Euclidean unit ball in C ⁿ . In this paper, we study several properties of strongly starlike mappings of order α (0 < α < 1) and bounded convex mappings on B ⁿ . We prove that K-quasiregular strongly starlike mappings of order α on B ⁿ have continuous and univalent extensions to ${\overline{B}^n}$ . We show that bounded convex mappings on B ⁿ are strongly starlike of some order α. We give a coefficient estimate for K-quasiregular strongly starlike mappings of order α on B ⁿ . Finally, we give examples of strongly starlike mappings of order α and bounded convex mappings on B ⁿ .     

在Banach空间中推广的Roper-Suffridge算子(Ⅰ)

本文将Cn中的Roper-Suffridge算子推广到任意复Banach空间中,并证明这种算子在任意复Banach空间中的某些区域上具有保持ε星形性,由此可以构造出任意复Banach空间,复Hilbert空间和Cn中的一些区域上的许多双全纯星形映照、双全纯凸映照、双全纯ε星形映照,同时,得到它们的增长定理等,将龚升与刘太顺,Roper与suffridge,Graham,Kohr等学者在Cn中的一些结果推广到任意复Banach空间或复Hilbert空间中．     

多复变数一类α次星形映射齐次展开式各项的精细估计

本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形.     

B_p上α凸映照

该文对当α≥0时给出Bp上α凸映照与星形映照之间的关系，给出一些Bp上α凸映照的例子.     

一类Reinhardt域上正规化双全纯完全准凸映射的分解定理

文主要研究Cⁿ 中一类有界凸的Reinhardt 域D_M上正规化双全纯完全准凸映射的齐次展式问题. 建立了D_M上完全准凸映射的分解定理, 并对D_M上星形映射进行一些探讨.     

Distortion theorems for subclasses of starlike mappings along a unit direction in ℂ

In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.     

GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ

In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results.     

有界凸圆型域上的准凸映照

本文研究星形映照的一类子族——有界凸圆型城上的准凸映照,并讨论了它与星形映照及凸映照的关系,建立其与凸映照同形的增长定理和掩盖定理．     

多复变数双全纯映照的一些偏微分不等式

本文在有界平衡域上建立一些与双全纯映照有关的偏微分不等式．作为应用，给出 有界平衡域上星形映照以及近似星形映照的一些充分判别条件．