On $H_3(1)$ Hankel determinant for some classes of univalent functions

By K. O. Babalola. 2009

201 citations recorded by the source corpus.

Focus in this paper is on the Hankel determinant, $H_3(1)$, for the well-known classes of bounded-turning, starlike and convex functions in the open unit disk $E=\{z\in \mathbb{C}\colon|z|<1\}$. The results obtained complete the series of research works in the search for sharp upper bounds on $H_3(1)$ for each of these classes.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/97bbf6757752294e3aad07b3a623dae76c09b2c5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain (2019, background): “The very first paper on H3,1 ( f ) was given in 2010 by Babalola [31], in which he obtained the upper bound of H3,1 ( f ) for the families of S∗, C, andR.”
Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain (2019, background): “Babalola [21] studied the Hankel determinant H3 (1) for some subclasses of normalized analytic functions in U.”
Third Hankel determinant for univalent starlike functions (2021, background): “In [1] it was proved that |H3(1)| ≤ 16.”
The Bound of the Hankel Determinant of the Third Kind for Starlike Functions (2018, background): “(b) Consider the case f3(c, x) < f4(c, x) in [1, 2] × [0, 1].”
Third Hankel Determinants for Subclasses of Univalent Functions (2017, background): “Moreover, Babalola claimed that the extremal functions for S∗ are the rotations of f(z) = z(1−z)2 .”
SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS (2019, unknown): “Many authors (see, for example, [1, 2, 4, 5, 11, 14]) have computed upper bounds for the functional J 2 , 3 over various subclasses of A .”