**Hari M. Srivastava 1,2,\*, Qazi Zahoor Ahmad 3, Nasir Khan 4, Nazar Khan <sup>3</sup> and Bilal Khan <sup>3</sup>**


Received: 29 January 2019; Accepted: 12 February 2019; Published: 15 February 2019

**Abstract:** By using a certain general conic domain as well as the quantum (or *q*-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U. In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic *q*-starlike functions. We also highlight some known consequences of our main results.

**Keywords:** analytic functions; starlike and *q*-starlike functions; *q*-derivative operator; *q*-hypergeometric functions; conic and generalized conic domains; Hankel determinant; Toeplitz matrices

**MSC:** Primary 05A30, 30C45; Secondary 11B65, 47B38
