论Szegǒ的定理

设f(z)=Z+a₂z²+…∈S.Szegǒ证明:S_n(z)=z+a₂z²+…+a_nzⁿ(n=2,3…)在|z|<1/4内单叶。ρ₀=1/4最好的,我们证明了更强的结果: 定理:若f(z)∈s.则s_n(z)(n=2,3…)在|z|<1/4内关于原点成星形。 当f∈S^*时为吴卓人所得。     

Subclasses of p-Valent Meromorphic Starlike Functions

Let M_(n p-1) denote the class of functions, regular and p-valent in the annulus 0 |z|<1 and satisfying where M_(n p) M_(n p-1) is proved. Since M_0 is the subclass of p-valent meromorphically starlike functions, all functions in M_(n p-1) are p-valent meromorphically starlike functions. Further the integrals of functions in M_(n p-1) are considered.     

强拟星函数的Fekete-Szeg?不等式

令T(β)表示β级强拟星函数类,f(z)=z+a₂z²+a₃z³+…∈T(β),对任意实参数μ,本文得到了|a₃-μa₂²|的准确上界.     

关于α阶星像函数类的一个子类

设f(z)=z+…在单位圆|z|<1内解析.给定λ(0≤λ<1),我们定义线性算子Ω^λ Ω^λf=Γ(2-λ)z^λD_z^λf(z);和Ω^n+λf=Ωⁿ(Ω^λf),n∈N∪{0}.其中D_z^λf(z)表示f(z)的分数阶导数且Ω¹ f(z)=zf′(z).用A_{n相似文献}   

Landau定理中的一个新上界

设f(z)=a₀+a₁z+…是单位圆内不取0与1的全纯函数.著名的Landau定理断言:存在一个与f无关的常数C使得|a₁|≤2|a₀|{|log|a₀||+C}.曾有许多数学家致力于估计此常数C.最后在1980年前后,由赖万才、Hempel及Jenkins独立地给出C的精确值:C=Γ⁴(1/4)/4π².本文的主要目的是要建立一种新形式的上界估计式以表明上述结果仍可改进.本文证明了: |a₁|≤2|a₀|{|log|a₀||+C-M|a₀ⁿ+1|²},其中M是一个与f无关的正的常数,而n取值为-1或1,依照|a₀|>1或≤1而定.     

Almansi-Type Decomposition Theorem for Bi-k-regular Functions in the Clifford Algebra Cl2n+2,0(R)*

Almansi-type decomposition theorem for bi-k-regular functions defined in a star-like domain Ω Rⁿ⁺¹ × Rⁿ⁺¹ centered at the origin with values in the Clifford algebra Cl_2n+_2,0(R) is proved. As a corollary, Almansi-type decomposition theorem for biharmonic functions of degree k is given.     

关于一类单叶函数

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B) of function f(z)=z+(?)a_nzⁿ satisfyingthe condition |(f′(z)-1)/(Bf′(z)-[B+(A-B)(1-α)])|<β for some α,β(0≤α<1,0<β≤1) and -1≤A相似文献   

用Hermite-Fejér型插值多项式逼近连续函数

Let f(x)∈C_[-1,1],T_n(x)=cos (n arccos x),U_n(x)=(sin((n+1)arccosx))/(1-x²)^1/2,P_n(x) be the Legendre polynomials of degree n. And let ω(t ) be a given modulus of continuity, H_ω={f|ω(f,t)≤ω(t)}.A. K. Sharma and J. Tzimbalario(J. Appro. Th., 13(1975), 431-442) considered the operators L_n,p (f, x) (p= 0, 1, 2,3) and obtained some theorems.In this paper, we prove the following theorems.     

具有缺项系数的几类解析函数族的性质

S*表示所有在单位圆盘 D 内解析且满足条件 f(0)=f′ (0)-1=0的星形函数族, K 表示所有在 D内解析且满足条件 f(0)=f′ (0)-1=0 的凸函数族, P 表示所有在 D 内解析且满足条件p(0)=1, Rep(z)>0 的函数族. 设P_n={p(z): p(z)=1+a_nzⁿ+a_n+1zⁿ⁺¹+…∈ P}, S*_n={f (z): f(z)=z+a_nzⁿ+a_n+1zⁿ⁺¹+…∈ S*}, K_n={f (z): f (z)=z+a_nzⁿ+a_n+1zⁿ⁺¹+…∈ K}. L_Sn*={g(z)=ln f(z)/z, f ∈ S_n*}, 其中对数函数取使得ln1=0的那个单值解析分支. 该文研究了函数族S_n^*, K_n和L_Sn*的性质, 找出了解析函数族L_Sn*的极值点与支撑点,并对S*_n与K_n的极值点和支撑点作了一些探讨.     

关于一类有理系数常微分方程的亚纯解

In this paper, we give an estimation of the number of meromorphic solu-tions and linearly independent meromorphic solutions of some class ordinary differential equations with rational coefficients (dw)/(dz)=a₀(z)+a₁(z)w+…+a_n(z)wⁿ (n≥3).