| Summary: | Very recently, functions that map the open unit disc <i>U</i> onto a limaçon domain, which is symmetric with respect to the real axis in the right-half plane, were initiated in the literature. The analytic characterization, geometric properties, and Hankel determinants of these families of functions were also demonstrated. In this article, we present a <i>q</i>-analogue of these functions and use it to establish the classes of starlike and convex limaçon functions that are correlated with <i>q</i>-calculus. Furthermore, the coefficient bounds, as well as the third Hankel determinants, for these novel classes are established. Moreover, at some stages, the radius of the inclusion relationship for a particular case of these subclasses with the Janowski families of functions are obtained. It is worth noting that many of our results are sharp.
|
|---|