Some properties of certain subclasses of meromorphically multivalent functions (original) (raw)

Some subclasses of meromorphically multivalent functions associated with a linear operator

Applied Mathematics and Computation, 2008

In the present paper, we introduce and investigate each of the following new subclasses: F q,s p,k (α; α 1 ; φ), G q,s p (α; α 1 ; φ) and H q,s p (α; α 1 ; φ) as well as F q,s p,k (α; α 1 ; φ), G q,s p (α; α 1 ; φ) and H q,s p (α; α 1 ; φ) * Corresponding author.

A class of meromorphically multivalent functions defined by means of a linear operator

Applied Mathematics and Computation, 2008

Let R p denote the class of functions of the form: f ðzÞ ¼ z Àp þ X 1 n¼1 a n z nÀp ðn 2 N ¼ f1; 2; 3;. . .gÞ; which are analytic in the punctured open unit disk U 0 ¼ fz : 0 < jzj < 1g. Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce a new subclass M p ða; c; k; hÞ of R p and investigate some properties for the class M p ða; c; k; hÞ.

Certain classes of meromorphic multivalent functions

Computers & Mathematics with Applications, 2009

In this paper, we introduce and investigate two new classes of meromorphic multivalent functions. Such results as subordination properties, coefficient inequalities, convolution properties and integral representations are proved. Several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived.

Subclasses of meromorphically multivalent functions defined by a differential operator

Computers & Mathematics with Applications, 2011

In this paper we introduce and study two new subclasses Σ λµmp (α, β) and Σ + λµmp (α, β) 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, δ)−neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.

Certain Class of Meromorphically Multivalent Functions Associated with a Linear Operator

SRI JNPG COLLEGE REVELATION A JOURNAL OF POPULAR SCIENCE

In this paper we have introduced a new subclass ( , , , , , ) ,, T a c A B p m l    of meromorphic p-valent functions in the punctured unit disk U*={z∈C:0 less than |z| less than 1} by sing a linear operator p m l I , , .Coefficients inequalities, Distortion theorems, Closure properties, Radii of starlikeness and convexity are obtained for this class. 2010 AMS CLASSIFICATION: Primary 30C45.

On Meromorphic Multivalent Functions Associated with Linear Operator

2021

The purpose of this article is to define and investigate a new subclass of meromorphic starlike functions by using Liu-Srivastava operator. A number of sufficient conditions for function belonging to this class are derived. 2010 Mathematics Subject Classification: Primary 30C45, Secondary 30C50

A Class of Meromorphic Multivalent Functions Defined by a Differential Operator

2016

In this paper, we define a class of meromorphically multivalent functions in U∗ = {z : z ∈ C : 0 < |z| < 1} by using a differential operator.Important properties of this class like coefficient estimates, distortion theorem, radius of starlikeness and convexity,closure theorems, convolution properties are obtained. We also study δ-neighboorhoods and partial sums for this class. 2010 Mathematics Subject Classification: 30C45.

Some Properties of Certain Classes of Meromorphic Multivalent Functions Defined by Subordination

Symmetry MDPI, 2023

In this paper, we define two classes of meromorphic multivalent functions in the punctured disc U∗ by using the principle of subordination. We investigate a number of useful results including subordination results, some connections with a certain integral operator, sandwich properties, an inclusion relationship, and Fekete-Szegö inequalities for the functions belonging these classes. Our results are connected with those in several earlier works, which are related to this field of Geometric Function Theory (GFT) of Complex Analysis.

Admissible Classes of Multivalent Meromorphic Functions Defined by a Linear Operator

Mathematics

The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For that, the appropriate classes of admissible functions are first defined. Based on these classes, we obtain some differential subordination and superordination results for multivalent meromorphic functions, analytic in the punctured unit disc, related to a linear operator ℑρ,τp(ν), for τ>0,ν,ρ∈C, such that Re(ρ−ν)≧0, Re(ν)>τp,(p∈N). Moreover, taking into account both subordination and superordination results, we derive a sandwich-type theorem. The connection with some other known results and an example are also provided.