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We introduce a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically functions related to Cho-Kwon-Srivastava operator. A characterization property giving the coefficient bounds is obtained for this class of functions. The other related properties, which are investigated in this paper, include distortion and the radii of starlikeness and convexity. We also consider several applications of our main results to generalized hypergeometric functions.

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity like a polynomial (i.e., these exceptional points must be poles and not essential singularities). A simpler definition states that a meromorphic function

In the present paper, we initiate the study of functions which are meromorphic in the punctured disk

Let

This paper is divided into two sections; the first introduces a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving linear operator. The second section highlights some applications of the main results involving generalized hypergeometric functions.

Let

For functions

The Hadamard product or convolution of the functions

By applying the subordination definition, we introduce here a new class

A function

As for the second result of this paper on applications involving generalized hypergeometric functions, we need to utilize the well-known Gaussian hypergeometric function. One denotes

Corresponding to the functions

Now, it follows from (

The subordination relation (

A function

In this section, we begin by proving a characterization property which provides a necessary and sufficient condition for a function

The function

Let

Conversely, if we assume that the inequality (

Theorem

If the function

We now state the following growth and distortion properties for the class

If the function

Since

We next determine the radii of meromorphic starlikeness and meromorphic convexity of the class

If the function

It suffices to prove that

If the function

By using the same technique employed in the proof of Theorem

The function

By using the same technique employed in the proof of Theorem

The following consequences of Theorem

If the function

If the function

If the function

The authors declare that there is no conflict of interests regarding the publication of this paper.

All authors read and approved the final paper.

The work here was fully supported by FRGSTOPDOWN/2013/ST06/UKM/01/1.