Third Hankel Determinants for Subclasses of Univalent Functions

By Pawel Zaprawa. 2017

148 citations recorded by the source corpus.

The main aim of this paper is to discuss the third Hankel determinants for three classes: $$S^*$$S∗ of starlike functions, $$\mathcal {K}$$K of convex functions and $$\mathcal {R}$$R of functions whose derivative has a positive real part. Moreover, the sharp results for twofold and threefold symmetric functions from these classes are obtained.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6bc6be5e87488ef4259631351da46331f0087a14

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dorina Raducanu
2. Pawel Zaprawa
3. Hari M. Srivastava

In Geometry and Topology

1. Dorina Raducanu
2. Pawel Zaprawa
3. Nanjundan Magesh
4. Hari M. Srivastava
5. J. Yamini
6. Halit Orhan

Citations in the corpus

• THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS (2018, unknown): “This result was improved by Zaprawa [23], using a suitable grouping and a result of Livingston [14,”
• The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛* (2019, unknown): “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): “…[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 estimates of | H ( 2 ) | are sharp, for example for the classes S ∗ or K consisting of starlike or convex functions, respectively,…”