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

• Published in: AIMS mathematics Vol. 6; no. 6; pp. 6580 - 6602
• Main Authors: Srivastava, H. M., Seoudy, T. M., Aouf, M. K.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2021
• Subjects: analytic functions; basic (or q-) calculus; coefficient estimates; conic domain; fekete-szegöinequalities; generalized conic domain; multivalent functions; principle of subordination
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021388

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.