On a Subclass of Meromorphic multivalent Functions associated with q-differential operator

Abstract

In this present paper, we have introduced and defined a new subclass of meromorphic multivalent function using the q-differential operator in punctured unit disk  We have obtained some geometric properties like coefficient inequality, a sufficient and necessary condition for the meromorphic multivalent functions to be in the class  and we have get a corollary from that theorem. Also, we have acquired the growth and distortion theorems bounds for the class Subsequently we have fixed the radii of starlikeness and convexity theorems. After that we have proved the class  is closed under convex linear combinations. Also, we have introduced the extreme points theorem and proved that. Finally, we have obtained arithmetic mean theorem in the same class.