Hankel and Toeplitz determinant for a subclass of multivalent q-starlike functions of order α

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.

Keywords

• quantum (or q-) calculus
• q-derivative operator
• multivalent functions
• q-starlike functions
• hankel determinant
• toeplitz matrices