Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain

Khan, Muhammad Ghaffar; Ahmad, Bakhtiar; Mashwani, Wali Khan; Shaba, Timilehin Gideon; Arif, Muhammad

doi:10.34198/ejms.6221.293308

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…Also, denote by S the class of univalent functions which are normalized by f(0) � f ′ (0) − 1 � 0, see [1,2]. Furthermore, suppose that N be the subclass of A consisting of functions with negative coefficients of the type:…”

Section: Introductionmentioning

confidence: 99%

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Univalent Functions by Means of Chebyshev Polynomials

Najafzadeh

Salleh

2022

Journal of Function Spaces

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The primary motivation of the paper is to define a new class C h δ α , β , γ which consists of univalent functions associated with Chebyshev polynomials. For this class, we determine the coefficient bound and convolution preserving property. Furthermore, by using subordination structure, two new subclasses of C h δ α , β , γ are introduced and denoted by M λ 1 , λ 2 , s and N λ 1 , λ 2 , s , respectively. For these subclasses, we obtain coefficient estimate, extreme points, integral representation, convexity, geometric interpretation, and inclusion results. Moreover, we prove that, under some restrictions on parameters, C h δ α , β , γ = N λ 1 , λ 2 , s .

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Section: Introductionmentioning

confidence: 99%

“…where t � cos θ and n is the degree of polynomial. For more details, one may refer to [1][2][3][4][5][6]. e polynomials in (4) are connected by the following relations:…”

Section: Introductionmentioning

confidence: 99%

Univalent Functions by Means of Chebyshev Polynomials

Najafzadeh

Salleh

2022

Journal of Function Spaces

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Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator

Rasheed Olawale Ayinla,

Ayotunde Olajide Lasode

2024

Malaya J. Mat.

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Abstract. In this exploration, we introduce a certain family of regular (or analytic) functions in association with the righthalf of the Lemniscate of Bernoulli and the well-known Opoola differential operator. For the regular function $f$ studied in this work, some estimates for the early coefficients, Fekete-Szegö functionals and second and third Hankel determinants are established. Another established result is the sharp upper estimate of the third Hankel determinant for the inverse function $f^{-1}$ of $f$.

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The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator

Srivástava

Shaba

Murugusundaramoorthy

et al. 2023

MATH

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<abstract>In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion: <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu^2z^2)e^{i\phi}\right)>0, \end{equation*} $\end{document} </tex-math></disp-formula> where $ z\in \mathbb{U} $, $ 0\leqq \mu\leqq 1 $ and $ \phi\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $, and which is associated with the Hohlov operator $ \mathcal{L}_{u, v}^{w} $. For functions in this class, the coefficient bounds, as well as upper estimates for the Fekete-Szegö functional and the Hankel determinant, are investigated.</abstract>

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Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain

Abstract: In this research article we consider two well known subclasses of starlike and bounded turning functions associated with nephroid domain. Our aims to find third Hankel determinant for these classes.

Cited by 3 publications

References 22 publications

Univalent Functions by Means of Chebyshev Polynomials

Univalent Functions by Means of Chebyshev Polynomials

Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator

The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator

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