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 $f(ξ) = f'(ξ) − 1 = 0, ξ (|ξ| = d)$ 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 function class $TS_ξ(α,β,γ)$. Further, we obtain integral means inequalities for the function $f ∈ TS_ξ(α,β,γ)$.