On certain classes of meromorphically multivalent functions associated with the generalized hypergeometric function

AbstractMaking use of a linear operator, which is defined here by means of the Hadamard product (or convolution), involving the generalized hypergeometric function, we introduce two novel subclasses Ωp,q,s(α1;A,B,λ) and Ωp,q,s+(α1;A,B,λ) of meromorphically multivalent functions of order λ(0≤λ<p) in the punctured disc U∗. In this paper we investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to the class Ωp,q,s+(α1;A,B,λ)