Bounds for the second Hankel determinant of certain univalent functions

By S. Lee, V. Ravichandran, Shamani Supramaniam. Journal of Inequalities and Applications, 2013

185 citations recorded by the source corpus.

The estimates for the second Hankel determinant a2a4−a32 of the analytic function f(z)=z+a2z2+a3z3+⋯ , for which either zf′(z)/f(z) or 1+zf″(z)/f′(z) is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike and lemniscate starlike functions are obtained. MSC:30C45, 30C80.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d880f55c1351830cd6c9bb13d55c9df0293df256

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In Geometry and Topology

1. Hari M. Srivastava
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Citations in the corpus

• Second Hankel determinant for close-to-convex functions (2017, background): “The majority of the results were obtained for H ( 2 ) = a a − a 32 , which is called the second Hankel determinant (see, for example, [1], [7], [8], [13], [22], [23]) There are, however, few papers that discuss the third Hankel determinant H ( 1 ) (see, for example: [2], [21], [24]) Although many…”
• THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS (2015, unknown): “[4, 11, 15, 16]).”
• THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS (2018, unknown): “Recently many authors have examined the Hankel determinant H 2 , 2 ( f ) = a 2 a 4 − a 23 of order 2 (see [4, 5, 8–10, , so the Hankel determinant H 2 , 1 ( f ) reduces to the well-known coe ffi cient functional which for S was estimated in 1916 by Bieberbach (see [7, Vol.”
• SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS (2019, unknown): “Many authors have examined the second Hankel determinant H 2 , 2 ( f ) = a 2 a 4 − a 23 (see, for example, [2, 4, 5, 10, 11, 17, 21]).”
• Second Hankel determinant for certain subclasses ofbi-univalent functions (2017, background): “In their paper [20], one can find the sharp bound for |H2(2)| for the functions in the classes of starlike functions of order β and convex functions of order β .”