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1.
本文研究了用Salagean算子定义的缺系数单叶调和函数类.利用从属关系和算子理论得到类中函数的系数估计、极值点、偏差定理、卷积性质、凸性组合与凸半径,推广了已有的一些结果.  相似文献   

2.
1980年,P.Duren和G.Schober引入了非零单叶函数族S_0,f∈S_0是指f(z)在单位园盘内单叶解析,恒不等于零并且用条件f(0)=1正规化。在后来的一系列文章中,他们研究了S_0的闭凸包HS_0中的线性极值问题。设ψ是S_0上的实值连续凸泛函,本文研究了凸极值问题maxψ(f)f∈S_0,得到极值函数值域及其不取弧的一些性质,这些结果包含了P.Duren和G.Schober的结果。  相似文献   

3.
李建林  魏广生 《数学学报》2002,45(5):847-850
设函数f(w)为凸区域D内的单叶解析函数,对于2≤n≤8和所有w∈D,本文得到估计式|f(n)(w)/f'(w)|的精确上界.这个结果推广了一些已知的结论.  相似文献   

4.
利用复的Hilbert空间中的Riesz基{xj}及其对偶Riesz基{yj},引入新的算子Φ({xj},{yj},{gj})(z),来构造出复的Hilbert空间中的单位球β上的一些双全纯凸映照或双全纯星形映照,利用复的Hilbert 空间中的框架理论,得到此算子的一些性质,给出由复平面C中的单位圆△上的单叶凸函数或单叶星形函数,来构造复的Hilbert 空间X中的单位球β上的双全纯凸映照或双全纯星形映照的一些具体例子,同时也引入一些双全纯凸映照或双全纯星形映照的子类.  相似文献   

5.
对任意给定的α∈[0,1),对单位圆盘D上规范化的保向调和映照类H的一个近于凸子类P~0(α)={f=h+g∈H:R{h′(z)-α}|g′(z)|,z∈D,g′(0)=0}的性质进行了研究,如P~0(α)类的凸像和星象半径估计、偏差定理、像域面积的估计、拟共形性,其中得到的凸像和星象半径估计值改进了文献[8-9]中相应结果.此外,对包含P~0(α)的稳定单叶调和映照类(SHU)的Pre-Schwarz导数进行了考虑,得到了精确的上界估计.  相似文献   

6.
我组一年来所指导的学生毕业论文,主要是单叶函数方面的,今将得到的结果,作一简要的叙述.  相似文献   

7.
研究了单位圆上具有像域线性连结性的局部单叶调和函数成为调和拟共形映照的充要条件,确定了一类具有线性连结像域的单叶调和函数的单叶调和稳定性参数区域,推广了Chuaqui和Hernández的相应结果.  相似文献   

8.
对数系数的估计在单叶函数的系数研究中有重要的意义.本文研究单叶函数一个子类C(A,B)中函数的对数系数.所得结果推广了一些已有的相关结果.  相似文献   

9.
在单复变函数的研究中,解析函数及调和函数的单叶性与保向性一直都是一个研究的主要问题.众所周知,调和函数f=h+g在单位圆盘U内局部单叶及保向当且仅当|h'(z)|>|g'(z)|.那么能否找到调和函数单叶保向的其它条件呢?引入了解析部分在不同区域上星象的调和函数的子类,并首次给出了相应函.数类上的调和函数单叶及保向的条件.所得结果进一步丰富几何函数论.  相似文献   

10.
引入了两类扩展的双单叶α-对数强凸函数族,利用分析的技巧研究了其Fekete-Szeg不等式.所得第三项系数估计改进了许多双单叶函数的已有结果.  相似文献   

11.
We define and investigate a new class of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convex combination and radii of convex for the above class of harmonic univalent functions.  相似文献   

12.
In this work the authors extend certain results concerning the Hadamard product for two classes related to starlike and convex univalent meromorphic functions with positive coefficients by using convolution.  相似文献   

13.
Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust's theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent analytic mappings, this family of convolution surfaces is much larger than just the family of associated surfaces. Also, this generalization guarantees that all the resulting surfaces are over close-to-convex domains. In particular, all the associate surfaces and certain Goursat transformation surfaces of a minimal graph over a convex domain are over close-to-convex domains.

  相似文献   


14.
《Mathematische Nachrichten》2018,291(10):1502-1513
We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro–Warschawski class of univalent functions as well as for the closed convex hulls of the convex and starlike functions by using an inequality from [6]. In particular, we generalize an inequality proved by Ma for starlike functions and answer a question from his paper [17]. Finally, we prove an asymptotic version of the generalized Zalcman conjecture for univalent functions and discuss various related or equivalent statements which may shed further light on the problem.  相似文献   

15.
It is well-known that the classes of starlike, convex and close-to-convex univalent functions are closed under convolution with convex functions. In this paper, closure properties under convolution of general classes of meromorphic p-valent functions that are either starlike, convex or close-to-convex with respect to n-ply symmetric, conjugate and symmetric conjugate points are investigated.  相似文献   

16.
本文主要讨论了带限制条件的正实部解析函数族及纯凸像函数族的一般极值问题.首先我们得了两类带限制条件的正实部函数族的支撑点的表达式.其次,我们讨论了亚纯凸像函数族的极值问题,得到了亚纯凸像函数族上Frchet可导泛函所对应的极函数的最好形式.  相似文献   

17.
The main object of this work is to extend the univalent condition for a family of integral operators. Several other closely-related results are also considered. A number of known univalent conditions would follow upon specializing the parameters involved in our main result.  相似文献   

18.
A general version of the Radó-Kneser-Choquet theorem implies that a piecewise constant sense-preserving mapping of the unit circle onto the vertices of a convex polygon extends to a univalent harmonic mapping of the unit disk onto the polygonal domain. This paper discusses similarly generated harmonic mappings of the disk onto nonconvex polygonal regions in the shape of regular stars. Calculation of the Blaschke product dilatation allows a determination of the exact range of parameters that produce univalent mappings.  相似文献   

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