On a New Class of Meromorphic Univalent Function Associated with Dziok _ Srivastava Operator

In this paper, we introduce and study a new class of meromorphic Univalent functions defined by Dziok_Srivastava operator for this class. We obtain coefficient inequality, convex set, closure and Hadamard product (or convolution).Further we obtain a neighborhood of the function , and the integral transform.


Introduction
, if .The linear operator defined in (1.5) is the Dziok_Srivastav operator see [8].Which contains the well define operators like Seoudy and Aouf [10], and see Dziok, Murugusundaramoorthy and Sokot [6], the saitoh generalized linear operator, the Bernardi_Libera Livingston operator and many others.

Definition( 1.1) Let
be given (1.2).The class is defined by the subclass of a consisting of functions of the form (1.2) and satisfying the analytic criterion | for and The present paper aims at providing a systematic investigation of various interesting properties and characteristics of function belonging to the new class .The properties such as the neighborhood, convex set, Hadamard product and integral operator defined on the new class are also discussed.

Coefficients Inequalities
First, in the following theorem, we obtain necessary and sufficient condition for a function to be in the class .
Theorem(2.1)Let be given by (1.2).Then if and only if for The result is sharp for the function Proof:-Assume that the inequality (2.1) holds true and let | | then from we have Hence, by maximum modulus principle, .
Conversely, suppose that , then from (2.2), we have We can choose the value of on the real axis, so that ( [ ] ) ( [ ] ) are real, upon clearly the denominator of (1.10) and letting , through real values .We get the inequality (2.1).Sharpness of the result follows be setting The proof is complete.

3.Closure on
Let the function be defined by Proof:-Since it follows from Theorem (2.1) that
The proof is complete.

Convex Set
Now, we state a theorem of convex set of the functions in the class Theorem (4.1)The class is convex set.
Proof:-let and be the arbitrary of .Then for every , we show that Thus we have The proof is complete.

Hadamard Product
We consider the Hadamard product (or convolution) of two power series Proof:-Note that For we have In order to obtain our result we have to find the largest such that So that The proof is complete.

Neighborhoods
The concept of neighborhood of analytic functions was first introduced by Goodman [7] and Ruscheweyh [9]

∑
Let denote the class of functions of the form: Which are analytic Meromorphic Univalent in the punctured unit disk | | .Let be a subclass of of function of the form ∑ The Hadamard product (or convolution) of two power series symbol defined, in terms of gamma function by The series in (1.7) converges absolutely for| | , if and for| |

∑
Now, we shall prove the following result for the closure of such a function in the class .
investigated this concept for the elements of several famous subclasses of analytic functions and Altintas and Owa[1]    considered for a certain family of analytic functions with negative coefficients, also Liu and Srivastava[8] and Atshan [3