A generalized conic domain and its applications to certain subclasses of analytic functions

Abstract

By using the idea of $q$-calculus, we generalize the conic domain and define various subclasses of analytic functions which map the open unit disk $$ \mathbb {U}= \{ z:z\in \mathbb {C} \text { and } \lvert z \rvert \lt 1 \} $$ onto this generalized conic domain. We study here some conspicuous results such as: coefficients estimates, sufficient condition and convolution properties for these newly defined classes. We consider various corollaries and consequences of our main results. Most of our results are connected with earlier works related to this field.