THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.

TRANSFORMS, DIFFERENTIAL SUBORDINATIONS AND A_p-WEIGHTED INEQUALITIES FOR BANACH-SPACE-VALUED REGULAR MARTINGALES

In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.

Some Applications of Differential Subordination of p-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.

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）.

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.

一类包含广义Mittag-Leffler函数的积分算子的从属与超从属结果

In the paper,by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function,the authors investigate subclasses of univalent analytic functions,such as starlike functions,convex functions,close-to-convex functions and quasiconvex functions.Several inclusion relationships,inequality properties,subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained.

Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers

Let p>2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality■for a large class of non-symmetric Fourier multipliers T_(m) obtained via modulation of jumps of certain Lévy processes.In particular,the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane.The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle.Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.

ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.

SANDWICH-TYPE RESULTS FOR A CLASS OF CONVEX INTEGRAL OPERATORS

Let H（U） be the space of analytic functions in the unit disk U. For the integral operator

Convexity Condition for a Class of Operator

In this paper,we find a subclass of starlike functions on the unit disk,which are mapped by a operator,given by F（z）=1＋u/zu∫z0 f（t）tu-1dt（Re u≥0）,onto convex functions.The main results extend some 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.

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 for these univalent functions, and some consequences involving well-known special functions are also presented.