A New Theoretical Investigation of the Generalized Formulations of Spirallike Functions

Abstract

In this study, the idea of $q$ -calculus is applied to define new classes of spirallike functions $\alpha -\text{UCSPT}\left(q,\varphi ,\delta \right)$ and $\alpha -S{P}_{p}T\left(q,\varphi ,\delta \right)$ . The coefficient inequalities, rotational invariance, and containment results are proved for these classes. Further, by introducing a parameter $\beta$ , two more subclasses are defined and their properties are investigated. Finally, we have probed into these classes by fixing finitely several coefficients.