Abstract
The aim of this paper is to define the operator of q-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of beta-uniformly starlike functions beta-S(alpha,q,lambda,delta). Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions f. beta-S(alpha,q,lambda,delta). We also determine the second Hankel inequality for functions belonging to this subclass.