Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli

By Mohsan Raza, S. Malik. Journal of Inequalities and Applications, 2013

118 citations recorded by the source corpus.

In this paper, the upper bound of the Hankel determinant H3(1) for a subclass of analytic functions associated with right half of the lemniscate of Bernoulli (x2+y2)2−2(x2−y2)=0 is investigated. MSC:30C45, 30C50.

Subfields: Applied Mathematics, Geometry and Topology, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/12ea39cbf9c79a66b22d4c69761be3d9c372803f

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In Applied Mathematics

In Geometry and Topology

In Physical and Theoretical Chemistry

Pawel Zaprawa

Citations in the corpus

The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛* (2019, background): “4), the upper bound of |H3(1)| can be obtained as follows: |H3(1)| ≤ |a3||H2(2)| + |a4||L|+ |a5||H2(1)|, (see [12, 21, 25, 27]).”
Second Hankel determinant for close-to-convex functions (2017, background): “…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 Hankel Determinants for Subclasses of Univalent Functions (2017, result): “Following this paper, some other authors published their results concerning |H3(1)| (see, for example, [14,17,18]).”
THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS (2015, background): “[27] M. Raza and S. N. Malik, Upper bound of the third Hankel determinant for a class of analytic functions related with Lemniscate of Bernoulli, J. Inequal.”