The Sharp Bounds of the Third-Order Hankel Determinant for Certain Analytic Functions Associated with an Eight-Shaped Domain

被引：22

作者：

Shi, Lei ^{[1
]}

Shutaywi, Meshal ^{[2
]}

Alreshidi, Naseer ^{[3
]}

Arif, Muhammad ^{[4
]}

Ghufran, Syed Muhammad ^{[4
]}

机构：

[1] Anyang Normal Univ, Sch Math & Stat, Anyang 455002, Peoples R China

[2] King Abdulaziz Univ, Coll Sci & Arts, Dept Math, Rabigh 21589, Saudi Arabia

[3] Northern Border Univ, Dept Math, Coll Sci, Ar Ar 73222, Saudi Arabia

[4] Abdul Wali Khan Univ Mardan, Dept Math, Mardan 23200, Pakistan

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 04期

关键词：

starlike function; bounded turning function; Hankel determinant problems; STARLIKE FUNCTIONS; RADIUS PROBLEMS; 3RD KIND; COEFFICIENTS; INVERSE;

D O I：

10.3390/fractalfract6040223

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main focus of this research is to solve certain coefficient-related problems for analytic functions that are subordinated to a unique trigonometric function. For the class S-sin*, with the quantity zf'(z)/f(z) subordinated to 1 + sin z, we obtain an estimate on the initial coefficient a(4) and an upper bound of the third Hankel determinant. For functions in the class BTsin, with f'(z) lie in an eight-shaped domain in the right-half plane, we prove that its upper bound of third Hankel determinant is 1/16. All the results are proven to be sharp.

引用

页数：21

共 48 条

[1] Starlikness Associated with Cosine Hyperbolic Function
Alotaibi, Abdullah
Arif, Muhammad
Alghamdi, Mohammed A.
Hussain, Shehzad
[J]. MATHEMATICS, 2020, 8 (07)
[2] Altinkaya S., 2016, TWMS J PURE APPL MAT, V5, P91
[3] Upper Bound of Second Hankel Determinant for Bi-BazilevicI† Functions
Altinkaya, Sahsene
Yalcin, Sibel
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (06) : 4081 - 4090
[4] Hankel determinant of order three for familiar subsets of analytic functions related with sine function
Arif, Muhammad
Raza, Mohsan
Tang, Huo
Hussain, Shehzad
Khan, Hassan
[J]. OPEN MATHEMATICS, 2019, 17 : 1615 - 1630
[5] A New Class of Analytic Functions Associated with Slgean Operator
Arif, Muhammad
Ahmad, Khurshid
Liu, Jin-Lin
Sokol, Janusz
[J]. JOURNAL OF FUNCTION SPACES, 2019, 2019
[6] Babalola KO, 2010, INEQUAL THEORY APPL, P1
[7] Starlike Functions Associated with Cosine Functions
Bano, Khadija
Raza, Mohsan
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2021, 47 (05) : 1513 - 1532
[8] THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS
Bansal, Deepak
Maharana, Sudhananda
Prajapat, Jugal Kishore
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 52 (06) : 1139 - 1148
[9] Sharp Bounds of the Coefficient Results for the Family of Bounded Turning Functions Associated with a Petal-Shaped Domain
Barukab, Omar M.
Arif, Muhammad
Abbas, Muhammad
Khan, Sher Afzal
[J]. JOURNAL OF FUNCTION SPACES, 2021, 2021
[10] Bieberbach L, 1916, SITZBER K PREUSS AKA, P940

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