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18 pages, 335 KB

Open AccessArticle

On Sharp Coefficients and Hankel Determinants for a Novel Class of Analytic Functions

by Dong Liu, Adeel Ahmad, Huma Ikhlas, Saqib Hussain, Saima Noor and Huo Tang

Axioms 2025, 14(3), 191; https://doi.org/10.3390/axioms14030191 - 5 Mar 2025

Cited by 1 | Viewed by 974

In this article, a new subclass of starlike functions is defined by using the technique of subordination and introducing a novel generalized domain. This domain is obtained by taking the composition of trigonometric

\sin e

function and the well known curve called lemniscate [...] Read more.

\sin e

function and the well known curve called lemniscate of Bernoulli which is the image of open unit disc under a function

g (ξ) = \sqrt{1 + ξ}

. This domain is characterized by its pleasing geometry which exhibits symmetric about the real axis. For this newly defined subclass, we investigate the sharp upper bounds for its first four coefficients, as well as the second and third order Hankel determinants. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)

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24 pages, 349 KB

Open AccessArticle

Sharp Coefficient Estimates for Analytic Functions Associated with Lemniscate of Bernoulli

by Rubab Nawaz, Rabia Fayyaz, Daniel Breaz and Luminiţa-Ioana Cotîrlă

Mathematics 2024, 12(15), 2309; https://doi.org/10.3390/math12152309 - 23 Jul 2024

Cited by 2 | Viewed by 1267

Abstract

The main purpose of this work is to study the third Hankel determinant for classes of Bernoulli lemniscate-related functions by introducing new subclasses of star-like functions represented by

S_{L λ}^{*}

and

R L_{λ}

. In many geometric and physical applications [...] Read more.

The main purpose of this work is to study the third Hankel determinant for classes of Bernoulli lemniscate-related functions by introducing new subclasses of star-like functions represented by

S_{L λ}^{*}

and

R L_{λ}

. In many geometric and physical applications of complex analysis, estimating sharp bounds for problems involving the coefficients of univalent functions is very important because these coefficients describe the fundamental properties of conformal maps. In the present study, we defined sharp bounds for function-coefficient problems belonging to the family of

S_{L λ}^{*}

and

R L_{λ}

. Most of the computed bounds are sharp. This study will encourage further research on the sharp bounds of analytical functions related to new image domains. Full article

(This article belongs to the Special Issue Current Topics in Geometric Function Theory)

12 pages, 309 KB

Open AccessArticle

Third Hankel Determinant for a Subfamily of Holomorphic Functions Related with Lemniscate of Bernoulli

by Halit Orhan, Murat Çağlar and Luminiţa-Ioana Cotîrlă

Mathematics 2023, 11(5), 1147; https://doi.org/10.3390/math11051147 - 25 Feb 2023

Cited by 8 | Viewed by 1673

Abstract

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant for a certain subclass

{SL}^{*} (u, v, α)

of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. [...] Read more.

The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant for a certain subclass

{SL}^{*} (u, v, α)

of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. Finally, for some special values of parameters, several corollaries were presented. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)

8 pages, 261 KB

Open AccessArticle

Third Hankel Determinant for a Subclass of Univalent Functions Associated with Lemniscate of Bernoulli

by Najeeb Ullah, Irfan Ali, Sardar Muhammad Hussain, Jong-Suk Ro, Nazar Khan and Bilal Khan

Fractal Fract. 2022, 6(1), 48; https://doi.org/10.3390/fractalfract6010048 - 16 Jan 2022

Cited by 4 | Viewed by 2773

Abstract

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant

H_{3} (1)

for this subclass by applying the Carlson–Shaffer operator to [...] Read more.

This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant

H_{3} (1)

for this subclass by applying the Carlson–Shaffer operator to it. The present work also deals with certain properties of this newly defined subclass, such as the upper bound of the Hankel determinant of order 3, coefficient estimates, etc. Full article

(This article belongs to the Special Issue New Trends in Geometric Function Theory)

10 pages, 271 KB

Open AccessArticle

Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

by Hari M. Srivastava, Qazi Zahoor Ahmad, Maslina Darus, Nazar Khan, Bilal Khan, Naveed Zaman and Hasrat Hussain Shah

Mathematics 2019, 7(9), 848; https://doi.org/10.3390/math7090848 - 14 Sep 2019

Cited by 40 | Viewed by 3344

Abstract

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk

U

that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the [...] Read more.

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk

U

that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered. Full article

(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)

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