On the Hankel determinants of univalent functions

Pommerenke, Ch.

doi:10.1112/s002557930000807x

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Introduction4

Bounds Of |H 3 (1)| For S * K and R1

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2016

2024

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Cited by 202 publications

(143 citation statements)

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“…Putting it into the definition of H 3 (1) for a convex function and applying the formulae (12) lead to H 3 (1) = G(p 1 , p 2 , p 3 , p 4 ), where…”

Section: Bounds Of |H 3 (1)| For S * K and Rmentioning

confidence: 99%

See 1 more Smart Citation

Third Hankel Determinants for Subclasses of Univalent Functions

Zaprawa

2016

Mediterr. J. Math.

111

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“…Putting it into the definition of H 3 (1) for a convex function and applying the formulae (12) lead to H 3 (1) = G(p 1 , p 2 , p 3 , p 4 ), where…”

Section: Bounds Of |H 3 (1)| For S * K and Rmentioning

confidence: 99%

“…It means that f has the expansion f (z) = z + ∞ n=2 a n z n . Pommerenke (see, [11,12]) defined the q-th Hankel determinant for a function f as: …”

Section: Introductionmentioning

confidence: 99%

Third Hankel Determinants for Subclasses of Univalent Functions

Zaprawa

2016

Mediterr. J. Math.

111

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“…The first one is known as the second Hankel determinant and it was examined in many papers. The investigation of Hankel determinants for analytic functions was started by Pommerenke (see [11,12]). Following Pommerenke, many mathematicians published their results concerning the second Hankel determinant for various classes of univalent functions (see, for example, [2,3,5,8,10]) or multivalent functions (see [9]).…”

Section: Introductionmentioning

confidence: 99%

On the Fekete-Szegö type functionals for starlike and convex functions

Zaprawa¹

2018

Turk J Math

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In the paper we discuss two functionals of the Fekete-Szegö type: Φ f (µ) = a2a4 − µa3 2 and Θ f (µ) = a4 − µa2a3 for an analytic function f (z) = z + a2z 2 + a3z 3 + . . . , z ∈ ∆ , ( ∆ = {z ∈ C : |z| < 1} ) and a real number µ .We focus our research on the estimation of |Φ f (µ)| and |Θ f (µ)| , while f is either in S * (the class of starlike functions) or in K (the class of convex functions).

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“…The second is called the second Hankel determinant. It was Pommerenke the first who studied this determinant in the geometric theory of analytic functions ( [6,7]). …”

Section: Introductionmentioning

confidence: 99%

On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials

2017

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Abstract. We solve problems concerning the coefficients of functions in the class T (λ) of typically real functions associated with Gegenbauer polynomials. The main aim is to determine the estimates of two expressions: |a4 − a2a3| and |a2a4 − a3 2 |. The second one is known as the second Hankel determinant. In order to obtain these bounds, we consider the regions of variability of selected pairs of coefficients for functions in T (λ). Furthermore, we find the upper and the lower bounds of functionals of Fekete-Szegö type. Finally, we present some conclusions for the classes T and T (1/2).Mathematics Subject Classification. 30C50.

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On the Hankel determinants of univalent functions

Cited by 202 publications

References 6 publications

Third Hankel Determinants for Subclasses of Univalent Functions

Third Hankel Determinants for Subclasses of Univalent Functions

On the Fekete-Szegö type functionals for starlike and convex functions

On Coefficients Problems for Typically Real Functions Related to Gegenbauer Polynomials

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