Hankel, Toeplitz, and Hermitian-Toeplitz Determinants for Certain Close-to-convex Functions

被引：23

作者：

Allu, Vasudevarao ^{[1
]}

Lecko, Adam ^{[2
]}

Thomas, Derek K. ^{[3
]}

机构：

[1] Indian Inst Technol Bhubaneswar, Sch Basic Sci, Jatni Rd, Bhubaneswar 752050, Odisha, India

[2] Univ Warmia & Mazury, Fac Math & Comp Sci, Dept Complex Anal, Ul Sloneczna 54, PL-10710 Olsztyn, Poland

[3] Swansea Univ Bay Campus, Dept Math, Swansea SA1 8EN, W Glam, Wales

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 01期

关键词：

Univalent functions; Ozaki close-to-convex functions; Hankel; Toeplitz; Hermitian-Toeplitz; determinants; coefficients; Zalcman functional; ZALCMAN CONJECTURE; STARLIKE; INEQUALITIES; COEFFICIENTS;

D O I：

10.1007/s00009-021-01934-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f be analytic in D = {z is an element of C : vertical bar z vertical bar < 1}, and be given by f(z) = z + Sigma(infinity)(n=2) a(n)z(n). We give sharp bounds for the second Hankel determinant, some Toeplitz, and some Hermitian-Toeplitz determinants of functions in the class of Ozaki close-to-convex functions, together with a sharp bound for the Zalcman functional J(2,3)(f).

引用

页数：17

共 24 条

[1] Extremal problems on the class of convex functions of order-1/2 [J].

Abu Muhanna, Yusuf ;

Li, Liulan ;

Ponnusamy, Saminathan .

ARCHIV DER MATHEMATIK, 2014, 103 (06) :461-471

[2] TOEPLITZ DETERMINANTS WHOSE ELEMENTS ARE THE COEFFICIENTS OF ANALYTIC AND UNIVALENT FUNCTIONS [J].

Ali, Md Firoz ;

Thomas, D. K. ;

Vasudevarao, A. .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2018, 97 (02) :253-264

[3] ON OZAKI CLOSE-TO-CONVEX FUNCTION [J].

Allu, Vasudevarao ;

Thomas, Derek K. ;

Tuneski, Nikola .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (01) :89-100

[4]

Babalola KO, 2010, INEQUAL THEORY APPL, P1

[5] THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS [J].

Bansal, Deepak ;

Maharana, Sudhananda ;

Prajapat, Jugal Kishore .

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 52 (06) :1139-1148

[6] CONVEX HULLS AND EXTREME POINTS OF FAMILIES OF STARLIKE AND CONVEX MAPPINGS [J].

BRICKMAN, L ;

HALLENBECK, DJ ;

MACGREGOR, TH ;

WILKEN, DR .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 185 (458) :413-428

[7] ON THE ZALCMAN CONJECTURE FOR STARLIKE AND TYPICALLY REAL FUNCTIONS [J].

BROWN, JE ;

TSAO, A .

MATHEMATISCHE ZEITSCHRIFT, 1986, 191 (03) :467-474

[8] Sharp Estimates of Generalized Zalcman Functional of Early Coefficients for Ma-Minda Type Functions [J].

Cho, Nak Eun ;

Kwon, Oh Sang ;

Lecko, Adam ;

Sim, Young Jae .

FILOMAT, 2018, 32 (18) :6267-6280

[9]

Cudna K, 2020, BOL SOC MAT MEX, V26, P361, DOI 10.1007/s40590-019-00271-1

[10]

Duren P. L., 1983, UNIVALENT FUNCTIONS, V259

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