Coefficient Estimates for Certain Subclasses of Bi-Univalent Ma-Minda Mocanu-Convex Functions

In this paper, we introduce and investigate a new subclass of the function class Σ of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several(known or new) consequences of the results are also pointed out.     

用Salagean算子定义的缺系数的单叶调和函数类

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.     

Double Subordination Preserving Properties for a New Generalized Srivastava-Attiya Integral Operator

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator.Differential sandwich-type theorems f...     

A subordination result involving Ruscheweyh derivatives and Hadamard product of certain classes of analytic functions

In the present paper we obtain an interesting subordination relation for a generalized subclass of analytic functions by using both the Hadamard product and Ruscheweyh derivatives. Some corollaries are also deduced as special cases of our main result.     

Close‐to‐convexity of normalized Dini functions

In this paper necessary and sufficient conditions are deduced for the close‐to‐convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some newly discovered Mittag–Leffler expansions for Bessel functions of the first kind.     

GENERALIZED WEAK FUNCTIONS

In this paper the authors introduce some new ideas on generalized numbers and generalized weak functions. They prove that the product of any two weak functions is a generalized weak function. So in particular they solve the problem of the multiplication of two generalized functions.     

Criteria for univalence of the Dziok-Srivastava and the Srivastava-Wright operators in the class A

In the geometric function theory (GFT) much attention is paid to various linear integral operators mapping the class S of the univalent functions and its subclasses into themselves. In [12] and [13] Hohlov obtained sufficient conditions that guarantee such mappings for the operator defined by means of Hadamard product with the Gauss hypergeometric function. In our earlier papers as [20], [19], [17] and [18], etc., we extended his method to the operators of the generalized fractional calculus (GFC, [16]). These operators have product functions of the forms _m+1F_m and _m+1Ψ_m and integral representations by means of the Meijer G- and Fox H-functions. Here we propose sufficient conditions that guarantee mapping of the univalent, respectively of the convex functions, into univalent functions in the case of the celebrated Dziok-Srivastava operator ([8] : J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput.103, No 1 (1999), pp. 1-13) defined as a Hadamard product with an arbitrary generalized hypergeometric function _pF_q. Similar conditions are suggested also for its extension involving the Wright _pΨ_q-function and called the Srivastava-Wright operator (Srivastava, [36]). Since the discussed operators include the above-mentioned GFC operators and many their particular cases (operators of the classical FC), from the results proposed here one can derive univalence criteria for many named operators in the GFT, as the operators of Hohlov, Carlson and Shaffer, Saigo, Libera, Bernardi, Erdélyi-Kober, etc., by giving particular values to the orders p ? q + 1 of the generalized hypergeometric functions and to their parameters.     

由卷积和从属关系刻画的单叶调和函数某些子类

Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new subclasses of SH consisting of univalent and sensepreserving functions defined by convolution and subordination. Sufficient coefficient conditions,distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity.     

Strong Differential Subordination and Superordination Properties of Phi-Like Functions

Strong differential subordination and superordination properties are determined for Phi-like functions in the open unit disk by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.     

Certain geometric properties of normalized Bessel functions

In this paper, we give a set of sufficient conditions for the normalized form of the generalized Bessel function to be univalent in the open unit disk, and further we obtain certain inequalities containing normalized Bessel functions.     

用Choi-Saigo-Srivastava算子定义的解析函数新子类

本文研究了用Choi-Saigo-Srivastava算子定义的一类解析函数.利用分析的方法和算子理论得到类中函数的积分表达式,偏差定理,卷积性质和半径问题.所得结果推广一些作者的相关结果.     

Subordination Results for p-Valent Meromorphic Functions Associated with a Linear Operator

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.     

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.     

ON UNIVALENT BLOCH FUNCTIONS

Let A = {z: lzl < 1} be the unit disk of complex plane C. For a 6 A, let W.(z) = isbe the M5biu8 transfOrlnation of A and let g(z, a) = log Ieel be the Green's functiou on Awith logarithlllic sillgularity at a E a. FOr 0 < p < oo, tl1e space Q. consists of all fuuctiolls fa11alytic il1 A for w11ichsup / I If'(z)l'(g(z, a))P dA(z) < oo, (1)aea j ja If'(z)l'(g(z, a))P dA(z) < oo, (1)wllere dA(z) is tlle Euclidcan area eIelllent o11 A.Q.-spaces have been i11vestigated by n1any authors (…     

Univalence of integral operators involving Bessel functions

In this note our aim is to deduce some sufficient conditions for integral operators involving Bessel functions of the first kind to be univalent in the open unit disk. The key tools in our proofs are the generalized versions of the well-known Ahlfors’ and Becker’s univalence criteria and some inequalities for the normalized Bessel functions of the first kind.     

On the univalence of an integral operator defined by Hadamard product

In this paper, we introduce a new general integral operator defined by the Hadamard product. Furthermore, we obtained new sufficient conditions for this operator to be univalent in the open unit disk.     

Subordination Results for ρ-Valent Meromorphic Functions Associated with a Linear Operator

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.     

A positive radial product formula for the Dunkl kernel

It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for nonnegative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radial here means that one of the factors in the product formula is replaced by its mean over a sphere. The key to this product formula is a positivity result for the Dunkl-type spherical mean operator. It can also be interpreted in the sense that the Dunkl-type generalized translation of radial functions is positivity-preserving. As an application, we construct Dunkl-type homogeneous Markov processes associated with radial probability distributions.

     

Series expansions for computing Bessel functions of variable order on bounded intervals

Based on a continuity property of the Hadamard product of power series we derive results concerning the rate of convergence of the partial sums of certain polynomial series expansions for Bessel functions. Since these partial sums are easily computable by recursion and since cancellation problems are considerably reduced compared to the corresponding Taylor sections, the expansions may be attractive for numerical purposes. A similar method yields results on series expansions for confluent hypergeometric functions. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Hadamard product of meromorphic univalent functions defined by using convolution

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.