%0 Journal Article
%T A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized Hypergeometric Functions
%A F. Ghanim
%A M. Darus
%J International Journal of Mathematics and Mathematical Sciences
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/374821
%X 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. 1. Introduction 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 is a function of the form where and are entire functions with (see [1, page 64]). A meromorphic function therefore may only have finite-order, isolated poles and zeros and no essential singularities in its domain. An equivalent definition of a meromorphic function is a complex analytic map to the Riemann sphere. For example, the gamma function is meromorphic in the whole complex plane . In the present paper, we initiate the study of functions which are meromorphic in the punctured disk with a Laurent expansion about the origin; see [2]. Let be the class of analytic functions with , which are convex and univalent in the open unit disk and for which For functions and analytic in , we say that is subordinate to and write if there exists an analytic function in such that Furthermore, if the function is univalent in , then 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. 2. Preliminaries Let denote the class of meromorphic functions normalized by which are analytic in the punctured unit disk . For , we denote by and the subclasses of consisting of all meromorphic functions which are, respectively, starlike of order and convex of order in . For functions £¿£¿ defined by we denote the Hadamard product (or convolution) of and by Cho et al. [3] and Ghanim and Darus [4] studied the following function: Corresponding to the function and using the Hadamard product for , we define a new linear operator on by The
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