C~n中单位多圆柱上一类B型α次准凸映射齐次展开式各项的精确估计

本文给出Cn中单位多圆柱上一类B型α次准凸映射f(z)齐次展开式各项的精确估计,其中f(z)=(f1(z),f2(z),...,fn(z))T是k折对称映射(或z=0是f(z)-z的k+1阶零点),且满足sup∥z∥=1,∥w∥=1∥Dmf(0)(zm-1,w)∥=sup∥z∥=1∥Dmf(0)(zm)∥,m=2,3,...所得到的估计包含已有文献的许多结论.     

Reinhardt域上一类推广的Roper-Suffridge算子

研究一类推广的Roper-Suffridge算子F(z)=(f(z_1)+f′(z_1)∑_(k=2)~nakz_k~pk,f′(z)1)(~1/p2)z_2,…,f′(z_1)~(1/pn)z_n)′,证明该算子在复欧氏空间中的Reinhardt域Ω_(n,p2,%…,pn)={z=(z_1,…,z_n)∈C~n:|z_|~2+∑_(k=2)~n|zk|~(pk)1,Pk∈N~+,k=2,…,n}上分别保持α次的殆β型螺形性,α次的β型螺形性及强β型螺形性.     

一类非线性复微分差分方程解的不存在性

该文研究了一类复微分差分方程[f(z)f'(z)]n + fm(z + r) = 1,[f(z)f'(z)]n + [f(z + r)-f(z)]m = 1,[f(z) f'(z)] 2 + P2(z) f2(z + η) = Q(z)eα(z) 的超越整函数解,其中P(z), Q(z)为非零多项式,α(z)为多项式,...     

多复变数完全拟凸映射的分解定理

设Ω_1C~(n1),Ω_2C~(n2)为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))'为Ω_1×Ω_2上的正规化全纯映射.本文证明f为Ω_1×Ω_2上的正规化双全纯完全拟凸映射当且仅当 f(z,w)=(Φ_1(z),Φ_2(w))'其中φj:Ωj→C~(nj)是Ωj(j=1,2)上的正规化双全纯完全拟凸映射。     

A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D.let Ωn,p1,p2,…,pn={z=(z1,z2,…,zn)'∈Cn:nΣj=1|zj|pj<1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers. In this paper,we will prove that Фn,β2,у2…βn,уn(f)(z)=(f(z1),(f(z1)z1)β2(f'(z1))у2z2,…,(f(z1)z1)βn(f'(z1))уnzn)' Preserves spirallikeness of type β and order α on Ωn,p1,p2,…pn.     

关于α次的β型螺形映照推广的Roper-Suffridge算子

对Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(0《α《1)次的β(-π/2《β《π/2)型螺形性进行了讨论.所得的结果推广了以前相应的结论.     

Reinhardt域上和复Hilbert空间单位球上推广的Roper-Suffridge算子

本文分别讨论Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(-π/2<α<π/2)型螺形性和保持α(0<α<1)次星形性.所得结果包含了已知对应的结论.     

Reinhardt域上和复Hilbert空间单位球上推广的Roper-Suffridge算子

本文分别讨论Cn中某一Reinhardt域上以及复Hilbert空间单位球上推广的Roper-Suffridge算子保持α(-π/2＜α＜π/2)型螺形性和保持α(0＜α＜1)次星形性.所得结果包含了已知对应的结论.     

The generalized Roper-Suffridge extension operator on bounded complete Reinhardt domains

The generalized Roper-Suffridge extension operator Ф(f) on the bounded complete Reinhardt domain Ω in Cn with n ≥ 2 is defined by Φrn,β2,γ2,…,βn,γn(f)(z)=(rf(z1/r),(rf(z1/r)/z1)β2(f'(z1/r))γ2z2,…,(rf(z1/r)/z1)βn(f'(z1/r)γnzn) for (z1,z2,…,zn) ∈Ω, where r = r(Ω) = sup{|z1| (z1,z2,…,zn) ∈ Ω},0 ≤ γj ≤ 1 -βj,0 ≤ βj ≤ 1,and we choose the branch of the power functions such that (f(z1)/z1)βj |z1=0 = 1 and (f′(z1))γj |z1=0 =1,j = 2,…,n. In this paper, we prove that the operator Фrn,β2,γ2,…,βn,γn(f) is from the subset of S*α(U) to S*α(Ω)(0 ≤ α ＜ 1) on Ω and the operator Фrn,β2,γ2,…, βn,γn(f) preserves the starlikeness of order α or the spirallikeness of type β on Dp for some suitable constantsβj,γj,pj, where Dp ={(z1,z2,…,zn) ∈ Cn ∑nj=1|zj|pj ＜ 1} (pj ＞ 0, j = 1,2,…,n), U is the unit disc in the complex plane C, and Sα* (Ω) is the class of all normalized starlike mappings of order α on Ω. We also obtain that Φrn,β2,γ2,…,γn(f) ∈ S*α(Dp) if and only if f ∈ S*a(U) for 0 ≤ α ＜ 1 and some suitable constants βj,γj,pj.     

$\mathbb{C}^n$中一类星形映射子族的增长定理及推广的Roper-Suffridge算子

在有界星形圆形域上定义了一个新的星形映射子族, 它包含了$\alpha$阶星形映射族和$\alpha$阶强星形映射族作为两个特殊子类. 给出了此类星形映射子族的增长定理和掩盖定理. 另外, 还证明了Reinhardt域$\Omega_{n,p_{2},\cdots,p_{n}}$上此星形映射子族在Roper-Suffridge算子 \begin{align*} F(z)=\Big(f(z_{1}),\Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{2}}(f'(z_{1}))^{\gamma_{2}}z_{2},\cdots, \Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{n}}(f'(z_{1}))^{\gamma_{n}}z_{n}\Big)' \end{align*} 作用下保持不变, 其中 $\Omega_{n,p_{2},\cdots,p_{n}}=\{z\in {\mathbb{C}}^{n}:|z_1|^2+|z_2|^{p_2}+\cdots + |z_n|^{p_n}<1\}$, $p_{j}\geq1$, $\beta_{j}\in$ $[0, 1]$, $\gamma_{j}\in[0, \frac{1}{p_{j}}]$满足$\beta_{j}+\gamma_{j}\leq1$, 所取的单值解析分支使得 $\big({\frac{f(z_{1})}{z_{1}}}\big)^{\beta_{j}}\big|_{z_{1}=0}=1$, $(f'(z_{1}))^{\gamma_{j}}\mid_{{z_{1}=0}}=1$, $j=2,\cdots,n$. 这些结果不仅包含了许多已有的结果, 而且得到了新的结论.