On differential Sandwich theorems of analytic functions defined by generalized Sălăgean integral operator

In this paper we obtain some applications of first order differential subordination and superordination results involving generalized S?l?gean integral operator for certain normalized analytic functions. Some of our results generalize previously known results.     

Subordination and superordination properties for a class of integral operators

In the present paper, we obtain some subordination- and superordinatiompreserving properties of certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorems for these integral operators are also considered.     

Certain family of integral operators preserving subordination and superordination

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.     

CERTAIN FAMILY OF INTEGRAL OPERATORS PRESERVING SUBORDINATION AND SUPERORDINATION

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.     

Subordination and superordination results associated with the generalized hypergeometric function

In the present investigation, we obtain some subordination and superordination results involving Hadamard products for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.     

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.     

Urn models and B-splines

Urn models are used to construct normalized B-spline basis functions over arbitrary knot vectors. These stochastic models are then applied to derive some of the basic analytic properties of B-splines. In particular, the Cox-de Boor recursion formula is given a probabilistic interpretation. The connection between urn models, B-splines, and Beta-splines is also discussed.     

Subordinations for Functions with Positive Real Part

Some sufficient conditions are determined for certain first order differential subordinations to imply the corresponding analytic solution is subordinate to a rational, exponential, or sine function. By applying these results, we also obtain sufficient conditions for normalized analytic functions to be in certain well known subclasses of starlike functions.     

A first-order differential double subordination with applications

Let q₁ and q₂ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions p to satisfy the double subordination chain q₁(z)?p(z)?q₂(z). The differential sandwich-type result obtained is applied to normalized univalent functions and to Φ-like functions.     

Minimal area problems for functions with integral representation

We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal areaa ₂-problem for convex functions and for typically real functions. The latter gives a new solution to the minimal areaa ₂-problem for the classS of normalized univalent functions in the unit disc. Supported by NSF grant DMS-0412908.     

Third-Order Differential Subordinations for Analytic Functions Associated with Generalized Mittag-Leffler Functions

In this paper, third-order differential subordination results are obtained for analytic functions associated with an operator defined by the normalized form of the generalized Mittag-Leffler functions. Some particular cases involving Mittag-Leffler and hyperbolic functions are also considered.     

Characterization of the determinant of a Laguerre matrix

A Toeplitz-like matrix has naturally occurred in the construction of iteration functions for finding zeroes of an analytic function. In this note, we study the properties of a Toeplitz-like matrix, and its relationship to the well known Toeplitz matrix involving normalized derivatives of an analytic function.     

Starlikeness of certain functions with integral representations

This paper is concerned with the starlikeness of certain normalized functions, analytic in the open unit disk, defined by integral representations. Results due to Caplinger and Singh are extended.     

Mapping properties of nonlinear integral operators and pre-Schwarzian derivatives

In this paper, nonlinear integral operators on normalized analytic functions in the unit disk are investigated in connection with the pre-Schwarzian derivative and the Hornich operation. In particular, several nontrivial relations between these operators and the class of strongly starlike functions will be deduced.     

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.     

非零单叶函数的极值问题

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。     

The construction of generalized B-spline low-pass filters related to possibility density

Starting from piecewise constant functions, a novel family of generalized symmetric B-splines, with realizable ideal low-pass filters, are constructed. The first order generalized B-spline low-pass filter is closely related to functions analytic in a neighborhood of the unit disc and the generalized sinc functions. The properties of this kind of low-pass filters are investigated. The behavior of the generalized B-spline low-pass filter related to normalized Gaussian distribution is considered.     

Equivariant functions and integrals of elliptic functions

In this paper, we introduce the theory of equivariant functions by studying their analytic, geometric and algebraic properties. We also determine the necessary and sufficient conditions under which an equivariant form arises from modular forms. This study was motivated by observing examples of functions for which the Schwarzian derivative is a modular form on a discrete group. We also investigate the Fourier expansions of normalized equivariant functions, and a strong emphasis is made on the connections to elliptic functions and their integrals.     

On discrete analytic functions: Products, rational functions and reproducing kernels

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.     

一类新的单叶调和函数(英文)

A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points.