New Subclass of Analytic Function Related with Generalized Conic Domain Associated with q − Differential Operator

Abstract

The quantum (or $q$ -) calculus is widely applied in various operators which include the $q$ -difference ( $q$ -derivative) operator, and this operator plays an important role in geometric function theory (GFT) as well as in the theory of hypergeometric series. In our present investigation, we introduce and study $q$ -differential operator associated with $q$ -Mittag–Leffler function which is an extension of the Salagean $q$ -differential operator. By using this newly defined operator, we define a new subclass of analytic function and studied certain subclass of analytic function in generalized conic domain ${\mathrm{\Omega }}_{k,q,\gamma }$ . For this class, we investigate structural formula, coefficient estimates, sufficient condition, Fekete–Szegö problem, and also some subordination results.