Starlike functions of complex order involving q-hypergeometric functions with fixed point

Abstract

Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with f (ξ) = f 0 (ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ C : |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the func tion class T S ξ (α, β, γ). Further, we obtain integral means inequalities for the function f ∈ T S ξ (α, β, γ).