Hankel and Toeplitz Determinants for a Subclass of <i>q</i>-Starlike Functions Associated with a General Conic Domain

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 <i>q</i>-starlike functions
• <i>q</i>-derivative operator
• <i>q</i>-hypergeometric functions
• conic and generalized conic domains
• Hankel determinant
• Toeplitz matrices