Subclasses of bi-univalent functions defined by convolution

In this paper, we introduced two new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution. Furthermore, we find estimates on the coefficients ∣a₂∣ and ∣a₃∣ for functions in these new subclasses.     

A study of a special family of analytic functions at infinity

In the present work we introduce certain new subclasses of analytic functions in the open unit disk U. Then by using a quasi-Hadamard product we discuss their applications in the space of analytic functions.     

Subordination properties of multivalent functions involving an extended fractional differintegral operator

The object of this article is to investigate inclusion, radius, and other various properties of subclasses of multivalent analytic functions, which are defined by using an extended version of the Owa-Srivastava fractional differintegral operator Ω(λ, p).     

The generalization of the generalized Al-Oboudi differential operator

In this paper, firstly we define the generalization of the generalized Al-Oboudi differential operator. Then we also define new classes of analytic and p-valently starlike and convex functions with complex order by means of this new general differential operator. Our main purpose is to determine coefficient bounds for functions in certain subclasses of this classes, which are introduced here by means of a family of nonhomogeneous Cauchy-Euler differential equations. Relevant connections of some of the results obtained with those in earlier works are also provided.     

Certain subclasses of p-valent functions involving the Dziok-Srivastava operator

Using the methods of differential subordination, we investigate some inclusion relationships of certain subclasses of analytic and p-valent functions which are defined by means of Dziok-Srivastava operator.     

Closure properties of operators on the Ma-Minda type starlike and convex functions

A normalized univalent function f is called Ma-Minda starlike or convex if zf^′(z)/f(z)?φ(z) or 1+zf^″(z)/f^′(z)?φ(z) where φ is a convex univalent function with φ(0)=1. The class of Ma-Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and close-to-convex functions. Connections with various earlier works are made.     

Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.     

Exclusive and essential sets of implicates of Boolean functions

In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions.     

近于凸函数新子类的偏差定理和卷积性质

引进了近于凸函数的新子类.利用从属关系得到了偏差定理和卷积性质.所得结果推广了一些作者的相关结果,并得到有趣的新结果.     

Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators

By making use of a general linear operator , the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses. Some interesting applications involving such and other families of linear operators are also considered. The results presented here include a number of known results as their special cases.     

Some subclasses of multivalent functions involving a certain linear operator

The authors investigate various inclusion and other properties of several subclasses of the class Ap of normalized p-valent analytic functions in the open unit disk, which are defined here by means of a certain linear operator. Problems involving generalized neighborhoods of analytic functions in the class Ap are investigated. Finally, some applications of fractional calculus operators are considered.     

积分算子作用下的亚纯多叶函数

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.     

无穷远点处亚纯单叶函数的拟Hadamard卷积(英文)

本文研究了圆环域U内亚纯星象和凸象函数的某些新子类的拟Hadamard卷积.利用卷积方法,获得了该类函数的与拟Hadamard卷积有关的某些性质,推广了一些已知结果.     

Convergence rate of Cesàro means of Fourier-Laplace series

The convergence rate of Fourier-Laplace series in logarithmic subclasses of L²(Σd) defined in terms of moduli of continuity is of interest. Lin and Wang [C. Lin, K. Wang, Convergence rate of Fourier-Laplace series of L²-functions, J. Approx. Theory 128 (2004) 103-114] recently presented a characterization of those subclasses and provided the almost everywhere convergence rates of Fourier-Laplace series in those subclasses. In this note, the almost everywhere convergence rates of the Cesàro means for Fourier-Laplace series of the logarithmic subclasses are obtained. The strong approximation order of the Cesàro means and the partial summation operators are also presented.     

Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations

Making use of a multiplier transformation, which is defined here by means of the Hadamard product (or convolution), the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties. Some integral-preserving properties in a given sector are also considered.     

Some applications of differential subordination of <Emphasis Type="Italic">p</Emphasis>-valent functions associated with Cho-Kwon-Srivastava operator

Making use of the principle of differential subordination, we investigate some inclusion relationships of certain subclasses of p-valent analytic functions which are defined by Cho-Kwon Srivast ava Operator.     

Coefficient bounds for some families of starlike and convex functions of complex order

In the present work, the authors determine coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy–Euler differential equations. Several corollaries and consequences of the main results are also considered.     

Properties of Some Families of Meromorphic Multivalent Functions Associated with Generalized Hypergeometric Functions

We introduce and study two subclasses ?_([α_1])(A, B, λ) and ?_([α_1])~+ (A, B, λ) of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main object is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products of functions belonging to the class ?_([α_1])~+(α, β, γ, λ).     

Some inclusion relationships and integral-preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators

The object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions. By making use of these novel integral operators, we introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex meromorphic functions. In particular, we establish some inclusion relationships associated with the aforementioned integral operators. Several interesting integral-preserving properties are also considered.