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.
Highlights
Introduction and DefinitionsLet the class of functions, which are analytic in the open unit diskU = {z : z ∈ C and| z | < 1}, be denoted by L (U)
Let A denote the class of all functions f, which are analytic in the open unit disk U and normalized by f (0) = 0 and f 0 (0) = 1
Suppose that S is the subclass of the analytic function class A, which consists of all functions which are univalent in U
Summary
Let P denote the well-known Carathéodory class of functions p, analytic in the open unit disk U, which are normalized by p (z) = 1 +. A. Ismail et al [12] were the first who used the q-derivative operator Dq to study the q-calculus analogous of the class S ∗ of starlike functions in U (see Definition 8 below). H2 (2) were obtained by several authors (see [18,19,20]) for various classes of functions It is well-known that the Fekete–Szegö functional a3 − a22 can be represented in terms of the Hankel determinant as H2 (1). Our focus is on the Hankel determinant and the Toeplitz matrices for the function class ST (k, λ, q) given by Definition 10
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