Hankel and Toeplitz Determinants for a Subclass of q-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.

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

“…The Hankel determinant plays a vital role in the theory of singularities [17] and is useful in the study of power series with integer coefficients (see [18][19][20]). Noteworthy, several authors obtained the sharp upper bounds on H 2 (2) (see, for example, [5,[21][22][23][24][25][26][27][28][29]) for various classes of functions. It is a well-known fact for the Fekete-Szegö functional that:…”

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

“…However, the exact estimate of this determinant for the family of close-to-convex functions is still undetermined [20]. Recently, Srivastava and his coauthors [21] found the estimate of the second Hankel determinant for bi-univalent functions involving the symmetric q-derivative operator, while in [22], the authors studied Hankel and Toeplitz determinants for subfamilies of q-starlike functions connected with the conic domain. For more literature, see [23][24][25][26][27][28][29][30].…”

A Study of Multivalent q-starlike Functions Connected with Circular Domain

“…347 et seq.]). The theory of q-starlike functions was later extended to various families of q-starlike functions by (for example) Agrawal and Sahoo [1] (see also the recent investigations on this subject by Srivastava et al [32,33,34,35,36,37]). Motivated by these q-developments in Geometric Function Theory, many authors such as like Srivastava and Bansal [29] were added their contributions in this direction which has made this research area much more attractive.…”