Second Hankel Determinant for a Subclass of Alpha Convex Functions

An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers

“…Several authors studied the determinant H q (n). In particular, sharp upper bounds on H 2 (2) were obtained in such earlier works as, for example, in [17,18] for various subclasses of the normalized analytic function class A. It is well-known for the Fekete-Szegö functional a 3 − a 2 2 that…”

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

“…Lemma 1 (see [20]). If the function p (z) given by (3) is in the Carathéodory class P of analytic functions with positive real part in U, then…”

“…, where a 1 = 1. In fact, this determinant has been studied by several authors, and sharp upper bounds on H 2 (2) were obtained by several authors (see [18][19][20]) for various classes of functions. It is well-known that the Fekete-Szegö functional a 3 − a 2 2 can be represented in terms of the Hankel determinant as H 2 (1).…”

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:…”