On the Second Hankel Determinant of Logarithmic Coefficients for Certain Univalent Functions

Allu, Vasudevarao; Arora, Vibhuti; Shaji, Amal

doi:10.1007/s00009-023-02272-x

Cited by 12 publications

(7 citation statements)

References 31 publications

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“…for starlike and convex functions with respect to symmetric points in the open unit disk U was considered by Allu and Arora [23].…”

Section: Second Hankel Determinant Of the Logarithmic Coefficients 481mentioning

confidence: 99%

Second Hankel determinant of the logarithmic coefficients for a subclass of univalent functions

Srivastava,

Eker,

Şeker

et al. 2024

MMN

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“…for starlike and convex functions with respect to symmetric points in the open unit disk U was considered by Allu and Arora [23].…”

Section: Second Hankel Determinant Of the Logarithmic Coefficients 481mentioning

confidence: 99%

Second Hankel determinant of the logarithmic coefficients for a subclass of univalent functions

Srivastava,

Eker,

Şeker

et al. 2024

MMN

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“…Very recently, Kowalczyk and Lecko [20] examined the sharp bounds of |H 2,1 (F f /2)| for the classes of strongly starlike and strongly convex functions. Allu et al [3] (see also [34]) examined the sharp bounds of |H 2,1 (F f /2)| for the classes of starlike and convex functions with respect to symmetric points. Moreover, the sharp bounds of |H 2,1 (F f /2)| for the class of starlike functions of order α (0 ≤ α < 1) with respect to symmetric points were investigated in [33].…”

Section: Introductionmentioning

confidence: 99%

Sharp bounds on Hankel determinants for Sakaguchi classes

Sun,

Kuang

2024

Preprint

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“…For σ = 0 the result of the Corollary 1 becomes Theorem 2.2 from [1]. Setting in Theorem 1 the function…”

mentioning

confidence: 98%

“…Further, due to the significance of the recent studies about the logarithmic coefficients, the problem obtaining the sharp bounds for the second Hankel determinant of these coefficients, that is H 2,1 (F f /2) was reported in the papers [1,8,9] for several subfamilies of analytic functions, where the second Hankel determinant for F f /2, by utilizing the relations (3), will be…”

mentioning

confidence: 99%

Sharp bounds of logarithmic coefficient problems for functions with respect to symmetric points

Mohammed

2023

Mat. Stud.

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The logarithmic coefficients play an important role for different estimates in the theory of univalent functions.Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the second Hankel determinant of these coefficients, that is $H_{2,1}(F_f/2)$ was paid attention. We recall that if $f$ and $F$ are two analytic functions in $\mathbb{D}$, the function $f$ is subordinate to $F$, written $f(z)\prec F(z)$, if there exists an analytic function $\omega$ in $\mathbb{D}$ with $\omega(0)=0$ and $|\omega(z)|<1$, such that $f(z)=F\left(\omega(z)\right)$ for all $z\in\mathbb{D}$. It is well-known that if $F$ is univalent in $\mathbb{D}$, then $f(z)\prec F(z)$ if and only if $f(0)=F(0)$ and $f(\mathbb{D})\subset F(\mathbb{D})$.A function $f\in\mathcal{A}$ is starlike with respect to symmetric points in $\mathbb{D}$ iffor every $r$ close to $1,$ $r < 1$ and every $z_0$ on $|z| = r$ the angular velocity of $f(z)$about $f(-z_0)$ is positive at $z = z_0$ as $z$ traverses the circle $|z| = r$ in the positivedirection. In the current study, we obtain the sharp bounds of the second Hankel determinant of the logarithmic coefficients for families $\mathcal{S}_s^*(\psi)$ and $\mathcal{C}_s(\psi)$ where were defined by the concept subordination and $\psi$ is considered univalent in $\mathbb{D}$ with positive real part in $\mathbb{D}$ and satisfies the condition $\psi(0)=1$. Note that $f\in \mathcal{S}_s^*(\psi)$ if\[\dfrac{2zf^\prime(z)}{f(z)-f(-z)}\prec\psi(z),\quad z\in\mathbb{D}\]and $f\in \mathcal{C}_s(\psi)$ if\[\dfrac{2(zf^\prime(z))^\prime}{f^\prime(z)+f^\prime(-z)}\prec\psi(z),\quad z\in\mathbb{D}.\]It is worthwhile mentioning that the given bounds in this paper extend and develop some related recent results in the literature. In addition, the results given in these theorems can be used for determining the upper bound of $\left\vert H_{2,1}(F_f/2)\right\vert$ for other popular families.

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On the Second Hankel Determinant of Logarithmic Coefficients for Certain Univalent Functions

Cited by 12 publications

References 31 publications

Second Hankel determinant of the logarithmic coefficients for a subclass of univalent functions

Second Hankel determinant of the logarithmic coefficients for a subclass of univalent functions

Sharp bounds on Hankel determinants for Sakaguchi classes

Sharp bounds of logarithmic coefficient problems for functions with respect to symmetric points

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