Convolution properties for certain classes of multivalent functions

AbstractRecently N.E. Cho, O.S. Kwon and H.M. Srivastava [Nak Eun Cho, Oh Sang Kwon, H.M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl. 292 (2004) 470–483] have introduced the class Sa,cλ(η;p;h) of multivalent analytic functions and have given a number of results. This class has been defined by means of a special linear operator associated with the Gaussian hypergeometric function. In this paper we have extended some of the previous results and have given other properties of this class. We have made use of differential subordinations and properties of convolution in geometric function theory

Differential Subordination And Superordination For Analytic And Meromorphic Functions Defined By Linear Operators [QA331. N219 2007 f rb].

Suatu fungsi f yang tertakrif pada cakera unit terbuka U dalam satah kompleks C disebut univalen jika fungsi tersebut memetakan titik berlainan dalam U ke titik berlainan dalam C. A function f defined on the open unit disk U of the complex plane C is univalent if it maps different points of U to different points of C

On inclusion relationships of certain subclasses of meromorphic functions involving integral operator

In this paper, we introduce some subclasses of meromorphic functions in the punctured unit disc. Several inclusion relationships and some other interesting properties of these classes are discussed

Some New Inclusion and Neighborhood Properties for Certain Multivalent Function Classes Associated with the Convolution Structure

We use the familiar convolution structure of analytic functions to introduce two new subclasses of multivalently analytic functions of complex order, and prove several inclusion relationships associated with the (,)-neighborhoods for these subclasses. Some interesting consequences of these results are also pointed out

Classes of Analytic Functions Defined by a Differential Operator Related to Conic Domains

Let A be the class of functions f(z) = z + ∑ k = 2∞ a k z k analytic in an open unit disc ∆. We use a generalized linear operator closely related to the multiplier transformation to study certain subclasses of A mapping ∆ onto conic domains. Using the principle of the differential subordination and the techniques of convolution, we investigate several properties of these classes, including some inclusion relations and convolution and coefficient bounds. In particular, we get many known and new results as special cases.Нехай A — клас функцій f(z) = z + ∑∞k = 2akzk, аналітичних у відкритому одиничному крузі Δ. До вивчення деяких підкласів A, що відображають Δ на конічні області, застосовано узагальнений лінійний оператор, тісно пов'язаний з перетворенням множення. За допомогою принципу диференціального підпорядкування та техніки згорток вивчено деякі властивості цих класів, що включають деякі співвідношення включення та згорток, а також оцінки для коефіцієнтів. Наприклад, низку відомих та нових результатів отримано як частинні випадки

Subclass of harmonic univalent functions defined by Dziok-Srivastava operator

In this paper we introduce a new class of harmonic univalent functions defined by the Dziok-Srivastava operator. Coefficient estimates, extreme points, distortion bounds and convex combination for functions belonging to this class are obtained and also for a class preserving the integral operator

Some properties for certain class of analytic functions defined by convolution

In this paper, we introduce a new class H_{T}(f,g;\alpha ,k) of analytic functions in the open unit disc U={z\in \mathbb{C}: left\vert z \right\vert <1} defined by convolution. The object of the present paper is to determine coefficient estimates, extreme points, distortion theorems, partial sums and integral means for functions belonging to the class H_{T}(f,g;\alpha ,k). We also obtain several results for the neighborhood of functions belonging to this class