k−uniformly multivalent functions involving Liu-Owa q−integral operator

Abstract

In this paper, we introduce q−analogue of Liu-Owa integral operator and define a subclass of k−uniformly multivalent starlike functions of order γ,(0 ≤ γ < p; p ∈ N) by using the Liu-Owa q−integral operator. We examine coefficient estimates, growth and distortion bounds for the functions belonging to the subclass of k−uniformly multivalent starlike functions of order γ . Moreover, we determine radii of k−uniformly starlikeness, convexity and close-to-convexity for the functions belonging to this subclass.