Hankel and Toeplitz determinant for a subclass of multivalent $ q $-starlike functions of order $ \alpha $

Abstract

<abstract> In this paper our aim is to study some valuable problems dealing with newly defined subclass of multivalent $ q $-starlike functions. These problems include the initial coefficient estimates, Toeplitz matrices, Hankel determinant, Fekete-Szego problem, upper bounds of the functional $ \left \vert a_{p+1}-\mu a_{p+1}^{2}\right \vert $ for the subclass of multivalent $ q $-starlike functions. As applications we study a $ q $-Bernardi integral operator for a subclass of multivalent $ q $-starlike functions. Furthermore, we also highlight some known consequence of our main results. </abstract>