G. MURUGUSUNDARAMOORTHY and K. UMA Certain subclasses of starlike functions of complex order involving the Hurwitz–Lerch Zeta function

Making use of the Hurwitz–Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by TS b (α, β, γ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class TS b (α, β, γ). In particular, we obtain integral means inequalities for the function f(z) belongs to the class TS b (α, β, γ) in the unit disc.