New subclass of <i>q</i>-starlike functions associated with generalized conic domain
Xiaoli Zhang, Shahid Khan, Saqib Hussain, Huo Tang, Zahid Shareef
Abstract
In this paper, the concepts of quantum (or <i>q</i>-) calculus and conic regions are combined to define a new domain Ω<sub><i>k, q, γ</i></sub> which represents the generalized conic regions. Then by using a certain generalized conic domain Ω<sub><i>k, q, γ</i></sub> we define and investigate a new subclass of normalized analytic functions in open unit disk <i>E</i>. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.