The sharp bound of the third Hankel determinant of the kth-root transformation for bounded turning functions

被引：0

作者：

Srivastava, Hari M. ^{[1
,2
,3
,4
,5
,6
]}

Rath, Biswajit ^{[7
]}

Kumar, K. Sanjay ^{[7
]}

Krishna, D. Vamshee ^{[8
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Kyung Hee Univ, Ctr Converging Humanities, 26 Kyungheedae Ro, Seoul 02447, South Korea

[4] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, Baku AZ-1007, Azerbaijan

[5] Int Telematic Univ Uninettuno, Sect Math, I-00186 Rome, Italy

[6] Chung Yuan Christian Univ, Dept Appl Math, Taoyuan City 320314, Taiwan

[7] GITAM Deemed Univ, GITAM Sch Sci, Dept Math, Visakhapatnam 530045, AP, India

[8] North Eastern Hill Univ NEHU, Dept Math, Shillong 793022, Meghalaya, India

来源：

ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA | 2023年 / 27卷 / 02期

关键词：

Univalent function; Hankel determinant; bounded turning func-tions; kth-root transformation; Carathe'odory function; ANALYTIC-FUNCTIONS; COEFFICIENT; INVERSE; KIND;

D O I：

10.12697/ACUTM.2023.27.15

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The objective of this paper is to estimate the sharp bound of the third Hankel determinant for the kth-root transformation to the class of functions whose derivative has a positive real part satisfying the normalized conditions f(0) = 0 and f'(0) = 1 in the open unit disk D := {z is an element of C : |z| < 1}.

引用

页码：185 / 210

页数：26

共 26 条

[1]

Ali RM, 2009, B IRAN MATH SOC, V35, P119

[2]

Babalola KO, 2010, INEQUAL THEORY APPL, P1

[3] THE SHARP BOUNDS OF THE SECOND AND THIRD HANKEL DETERMINANTS FOR THE CLASS SL [J].

Banga, Shagun ;

Kumar, S. Sivaprasad .

MATHEMATICA SLOVACA, 2020, 70 (04) :849-862

[4]

Caratheodory C., 1911, Rendiconti del Circolo Matematico di Palermo, V32, P193, DOI DOI 10.1007/BF03014795

[5]

Duren P., 1983, Grundlehren der Mathematischen Wissenschaften, V259

[6]

Goodman AW., 1983, Univalent Functions, Vol 1 and Vol 2

[7]

Hayami T., 2010, Int. J. Math. Anal, V4, P2573

[8] The sharp bound of the third Hankel determinant for functions of bounded turning [J].

Kowalczyk, Bogumila ;

Lecko, Adam .

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2021, 27 (03)

[9] THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS [J].

Kowalczyk, Bogumila ;

Lecko, Adam ;

Sim, Young Jae .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2018, 97 (03) :435-445

[10] The Sharp Bound of the Third Hankel Determinant for the Inverse of Bounded Turning Functions [J].

Kumar, Sanjay K. ;

Rath, Biswajit ;

Krishna, Vamshee D. .

CONTEMPORARY MATHEMATICS, 2023, 4 (01) :30-41

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