A generalized conic domain and its applications to certain subclasses of multivalent functions associated with the basic (or q-) calculus

Abstract

In this paper, by using the concept of the basic (or $ q $-) calculus and a generalized conic domain, we define two subclasses of normalized multivalent functions which map the open unit disk: $ \mathbb{U} = \left\{z: z\in \mathbb{C}\qquad \text{and} \qquad \left\vert z\right\vert <1\right\} $ onto this generalized conic domain. We investigate a number of useful properties including (for example) the coefficient estimates and the Fekete-Szegö inequalities for each of these multivalent function classes. Our results are connected with those in several earlier works which are related to this field of Geometric Function Theory of Complex Analysis.

Keywords

• analytic functions
• multivalent functions
• conic domain
• basic (or q-) calculus
• generalized conic domain
• principle of subordination
• coefficient estimates
• fekete-szegöinequalities