Subclasses of Analytic Functions of Complex Order Involving Jackson’s (p, q)-derivative

Abstract

In this paper, we introduce a new differential operator defined by the Jackson’s (p, q)-derivative. Making use of this differential operator, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. For this subclass, we obtain coefficient estimates, extreme points, and integral means inequalities. Furthermore, we obtain some distortion theorems involving fractional integrals and fractional derivatives. Several special cases of our results are also pointed out.