Second Hankel Determinant for a Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

In this paper, we consider the class of strongly bi-close-to-convex functions of order α and bi-close-to-convex functions of order β. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.

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Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials

Asian-European Journal of Mathematics ◽

10.1142/s1793557119500177 ◽

2019 ◽

Vol 12 (02) ◽

pp. 1950017

Author(s):

H. Orhan ◽

N. Magesh ◽

V. K. Balaji

Keyword(s):

Unit Disk ◽

Upper Bound ◽

Chebyshev Polynomials ◽

Univalent Functions ◽

Function Class ◽

Open Unit ◽

Open Unit Disk ◽

Hankel Determinant ◽

Second Hankel Determinant ◽

Upper Bound Estimate

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [Formula: see text] of analytic bi-univalent function class [Formula: see text] which is associated with Chebyshev polynomials in the open unit disk.

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An upper bound to the nonlinear functional for certain subclasses of analytic functions associated with Hankel determinant

Asian-European Journal of Mathematics ◽

10.1142/s1793557113500423 ◽

2014 ◽

Vol 07 (02) ◽

pp. 1350042

Author(s):

D. Vamshee Krishna ◽

T. Ramreddy

Keyword(s):

Upper Bound ◽

Convex Functions ◽

Analytic Functions ◽

Hankel Determinant ◽

Toeplitz Determinants ◽

Nonlinear Functional ◽

Determinant Formula ◽

Starlike And Convex Functions ◽

Second Hankel Determinant ◽

Strongly Starlike

The objective of this paper is to obtain an upper bound to the second Hankel determinant [Formula: see text] for the functions belonging to strongly starlike and convex functions of order α(0 < α ≤ 1). Further, we introduce a subclass of analytic functions and obtain the same coefficient inequality for the functions in this class, using Toeplitz determinants.

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The second Hankel determinant for strongly convex and Ozaki close-to-convex functions

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/s10231-021-01089-3 ◽

2021 ◽

Author(s):

Young Jae Sim ◽

Adam Lecko ◽

Derek K. Thomas

Keyword(s):

Unit Disk ◽

Convex Functions ◽

Univalent Functions ◽

Inverse Function ◽

Invariance Property ◽

Hankel Determinant ◽

Sharp Bounds ◽

Strongly Convex Functions ◽

Strongly Convex ◽

Second Hankel Determinant

AbstractLet f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1 \}$$ D = { z ∈ C : | z | < 1 } , and $${{\mathcal {S}}}$$ S be the subclass of normalized univalent functions given by $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n$$ f ( z ) = z + ∑ n = 2 ∞ a n z n for $$z\in {\mathbb {D}}$$ z ∈ D . We give sharp bounds for the modulus of the second Hankel determinant $$ H_2(2)(f)=a_2a_4-a_3^2$$ H 2 ( 2 ) ( f ) = a 2 a 4 - a 3 2 for the subclass $$ {\mathcal F_{O}}(\lambda ,\beta )$$ F O ( λ , β ) of strongly Ozaki close-to-convex functions, where $$1/2\le \lambda \le 1$$ 1 / 2 ≤ λ ≤ 1 , and $$0<\beta \le 1$$ 0 < β ≤ 1 . Sharp bounds are also given for $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | , where $$f^{-1}$$ f - 1 is the inverse function of f. The results settle an invariance property of $$|H_2(2)(f)|$$ | H 2 ( 2 ) ( f ) | and $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | for strongly convex functions.

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Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v37i4.32701 ◽

2018 ◽

Vol 37 (4) ◽

pp. 83-95

Author(s):

Trailokya Panigrahi ◽

Janusz Sokól

Keyword(s):

Upper Bound ◽

Analytic Functions ◽

Hankel Determinant ◽

Lemniscate Of Bernoulli ◽

Toeplitz Determinant ◽

Second Hankel Determinant ◽

Coefficient Inequalities ◽

The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*} associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}| for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

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Study of Second Hankel Determinant for Certain Subclasses of Functions Defined by Al-Oboudi Differential Operator

Baghdad Science Journal ◽

10.21123/bsj.2020.17.1(suppl.).0353 ◽

2020 ◽

Vol 17 (1(Suppl.)) ◽

pp. 0353

Author(s):

K. A. Challab et al.

Keyword(s):

Differential Operator ◽

Upper Bound ◽

Unit Disc ◽

Hankel Determinant ◽

Special Cases ◽

Second Hankel Determinant

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

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The Second Hankel Determinant Problem for a Class of Bi-Close-to-Convex Functions

Mathematics ◽

10.3390/math7100986 ◽

2019 ◽

Vol 7 (10) ◽

pp. 986 ◽

Cited By ~ 1

Author(s):

Nak Eun Cho ◽

Ebrahim Analouei Adegani ◽

Serap Bulut ◽

Ahmad Motamednezhad

Keyword(s):

Convex Functions ◽

Hankel Determinant ◽

Second Hankel Determinant ◽

Class C ◽

Proof Methods

The purpose of the present work is to determine a bound for the functional H 2 ( 2 ) = a 2 a 4 − a 3 2 for functions belonging to the class C Σ of bi-close-to-convex functions. The main result presented here provides much improved estimation compared with the previous result by means of different proof methods than those used by others.

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