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

Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions is defined. Making use of the operator $\mathrm{{\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l),$ two new subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out

Subclasses of meromorphically multivalent functions defined by a differential operator

In this paper we introduce and study two new subclasses \Sigma_{\lambda\mu mp}(\alpha,\beta)$and$\Sigma^{+}_{\lambda\mu mp}(\alpha,\beta)$of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of$% (n,\delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

Certain classes of multivalent functions with negative coefficients associated with a convolution structure

Making use of a convolution structure, we introduce a new class of analytic functions $mathbb{T}^{p}_{g}(lambda,alpha, beta, )$ defined in the open unit disc and investigate its various characteristics. Further we obtained distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to the class $mathbb{T}^{p}_{g}(lambda,alpha, beta).

Some Geometric Properties Of Multivalent Convex Function For Operator On Hilbert Space

بالاستفادة من استعمال المؤثر على فضاء هلبرت، نحنُ  قدمنا ودرسنا بعض الخصائص الهندسية من الدوال التحليلية المتعددة التكافؤ المحدبة ذات معاملات سالبة.  للصنف الجزئي كذلك حصلنا على بعض الخصائص الهندسية، مثل، متراجحة المعاملات، مبرهنة النمو والتشوية، النقاط الحرجة، المجموعة المحدبة، نظرية الانغلاق، أنصاف الاقطار المغلقة، المتوسط الوزني وخواص الاحتواء لهذا الصنف.              By making use of the operator on Hilbert space, we introduce and study some properties of geometric of a subclass of multivalent convex functions with negative coefficients. Also, we obtain some geometric properties, such as coefficient inequality, growth and distortion theorem, extreme points, convex set, closure theorem, radius of close-to-convexity, weighted mean and inclusive properties

New Criteria for Meromorphic Multivalent Alpha-Convex Functions

The aim of the present paper is to obtain sufficient condition for the class of meromorphic p-valent alpha convex functions of order ξ and then to study mapping properties of the newly defined integral operators. Many known results appeared as special consequences of our work

Inclusion Properties on a Class of Meromorphic Functions Defined by a Linear Operator

In the present paper, we study a certain class of meromorphic univalent functions f(z) dened by the linear operator L(α,β) f (z). The aim of the present paper is to prove some properties for the class Σα,β,kλ;(h) to satisfy the certain subordination.AMS Subject Classication: 30C4