Certain subclasses of meromorphically $q$-starlike functions associated with the $q$-derivative operators

UDC 517.5 The purpose of the present paper is to establish several general results concerning the partial sums of meromorphically starlike functions defined here by means of a certain class of $q$-derivative (or $q$-difference) operators. The familiar concept of neighborhood for meromorphic functions are also considered. Moreover, by using a Ruscheweyh-type $q$-derivative operator, we define and study another new class of functions emerging from the class of normalized meromorphic functions.