Second Hankel determinants for the class of typically real functions
type: Item
instance of: scholarly article
title: Second Hankel determinants for the class of typically real functions
zbMATH Open document ID: 1470.30023
DOI: 10.1155/2016/3792367
author: Paweł Zaprawa
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: We discuss the Hankel determinants \(H_2(n) = a_n a_{n + 2} - \left(a_{n + 1}\right)^2\) for typically real functions, that is, analytic functions which satisfy the condition \(\operatorname{Im} z \operatorname{Im} f(z) \geq 0\) in the unit disk \(\Delta\). Main results are concerned with \(H_2(2)\) and \(H_2(3)\). The sharp upper and lower bounds are given. In general case, for \(n \geq 4\), the results are not sharp. Moreover, we present some remarks connected with typically real odd functions.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C50
Mathematics Subject Classification ID: 30C75
zbMATH DE Number: 6929363
Wikidata QID: Q59121526
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3792367
OpenAlex ID: W2265945549
cites work: On the Coefficients and Hankel Determinants of Univalent Functions
cites work: On the Hankel determinants of univalent functions
cites work: Q5433695
cites work: Q5442802
cites work: Bounds for the second Hankel determinant of certain univalent functions
cites work: Hankel determinant for starlike and convex functions of order alpha
cites work: Q3456285
cites work: Q4840631
cites work: Q4352061
cites work: Upper bound of second Hankel determinant for certain subclasses of analytic functions
cites work: Second Hankel determinant for a class of analytic functions defined by fractional derivative
cites work: On the Hankel Determinants of Areally Mean p -Valent Functions
cites work: Q3097203
cites work: Third Hankel determinant for \(\alpha\)-starlike functions
cites work: Q5591649
cites work: On the coefficients of a typically-real function
cites work: Q3704135
cites work: Generalized Zalcman conjecture for starlike and typically real functions
cites work: Q3336024
description: scientific article; zbMATH DE number 6929363