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1.
Let
denote the generalized hypergeometric function
where no denominator parameter can be zero or a negative integer and (a,n) denotes the ascending factorial notation. Ponnusamy and Vuorinen raised the problem of finding conditions on the parameters aj > 0, bj > 0 so that the function
is univalent in . The main aim of this paper is to discuss this problem in detail for the case q = 2. 相似文献
2.
In the present paper, we introduce some new subclasses of meromorphic starlike,convex, close-to-convex and quasi-convex functions of β-reciprocal in terms of the linear operator using subordination. We obtain the coefficient estimates, convolution properties, integral preserving properties and inclusion relationships of the classes. The results presented here include several results as their special cases. 相似文献
3.
令∑_p表示形如f(z)=z~(-p)+∑m=1∞(p∈N={1,2,3…})且在去心单位开圆盘D=U\{0}={z∶z∈C且0|z|1}上解析的亚纯多叶函数类.利用一个作用在∑_p上的乘积算子定义了几个新的亚纯函数的子类,并考虑这些函数类在积分算子作用下的性质. 相似文献
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In this paper we introduce and study some new subclasses of meromorphic starlike multivalentfunctions.Inclusion relations are established,Integral transforms of functions in these classes are alsoconsidered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra[3],Goel and Sohe[4]and Bajpai[5]. 相似文献
6.
In this paper, by making use of the Hadamard products, we obtain some subordination results for certain family of meromorphic functions defined by using a new linear operator. 相似文献
7.
设(ぁ)为区域D上的一族亚纯函数,a,b为互相判虽的两个复数.若对(ぁ)中任意函数f,f在D内的极点重数至少为2,且当f(z)=a时,f'(z)=a;f(z)=b时f'(z)=b,则(ぁ)在D内正规. 相似文献
8.
Subordination Results for ρ-Valent Meromorphic Functions Associated with a Linear Operator 下载免费PDF全文
A. O. Mostafa & M. K. Aouf 《分析论及其应用》2014,30(4):369-376
In this paper, by making use of the Hadamard products, we obtain some subordination results for certain family of meromorphic functions defined by using a new linear operator. 相似文献
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对复平面C的非空有限子集S_1和S_2,记在复平面区域D内满足{z∈D:f(z)∈S_1}={z∈D:f′(z)∈S_2}的全体亚纯函数f形成的函数族为D,那么当S_1和S_2共有至少12个元素对函数族D正规.特别地,当S_1具有至少三个复数时,我们得到了准确的结果. 相似文献
11.
In this paper we give analogues of the Ramanujan functions and nonlinear differential equations for them. Investigating a modular structure of solutions for nonlinear differential systems, we deduce new identities between the Ramanujan and hypergeometric functions. Another result of this paper is a solution of transcendence problems concerning nonlinear systems. 相似文献
12.
设F为区域D内的一族亚纯函数,对于每个f∈F,f的所有极点重数至少是2,a(z)和b(z)为两个在D内满足a(z)■b(z)的全纯函数.若对于每个f∈F,f(z)≠a(z)和f(z)≠b(z),则F在D内正规.这个结果改进了经典的Montel定则.此外,我们也讨论了亚纯函数族中每个函数与其导函数分担两个全纯函数的正规性. 相似文献
13.
利用Dziok-Srivastava算子定义了单位圆盘内以原点为极点的具有正系数的p叶亚纯函数的子类Wp+,q,s(α1,α),考察它们的各种性质,并将解析函数的邻域概念运用于此亚纯多叶函数类. 相似文献
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指出文献 [2 ]和文献 [4]中的错误 ,并且得到含有单位圆盘内接解析函数与亚纯函数的几个不等式 . 相似文献
16.
In this paper we introduce an estimation, namely, the upper bounds of the order and type, logarithmic order and logarithmic type and q-order and q-type of generalized Hadamard product of functions of the complex variables z. We append this study by getting a result concerning the subject of linear substitution. 相似文献
17.
本文研究亚纯函数的弱斥性不动点与拟正规族的关系,得到了以下结果: 设F是区域D内的亚纯函数族,q是一个非负整数。如果对任意f∈F,存在自然数k=k(f)>1,使得f的k次迭代fk在D内最多只有q个弱斥性不动点,则F是D内阶至多为max{4,q+2}的拟正规族。 相似文献
18.
The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation 下载免费PDF全文
A formula for the mean-value distribution of certain meromorphic functions on a vertical line s = σ +iR under a generalized Boolean transformation, called rational Boolean transformation from R into itself, is derived using Birkhoff 's ergodic theorem. This formula is represented as a computable integral. Using the Cauchy's integral theorem, values of this integral corresponding to various possible cases are explicitly computed. 相似文献
19.
In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this paper improve some previous results. 相似文献
20.
引进了去心圆盘U~*={z:0|z|1}内的亚纯倒星象函数和倒凸象函数的某些新子类,研究了该类中函数的拟Hadamard卷积,所得结果推广了前人的某些工作. 相似文献