Hankel Determinant and Toeplitz Determinant on the Class of Bazilevič Functions Related to the Bernoulli Lemniscate

Ni Made Asih; Sa’adatul Fitri; Ratno Bagus Edy Wibowo

doi:10.29020/nybg.ejpam.v16i2.4772

Hankel Determinant and Toeplitz Determinant on the Class of Bazilevič Functions Related to the Bernoulli Lemniscate

Ni Made Asih^*
, Sa’adatul Fitri
, Ratno Bagus Edy Wibowo
, Marjono

^*Corresponding author for this work

Faculty of Mathematics and Natural Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this papers, we investigate the Hankel determinant and Toeplitz determinant for the class Bazilevič Function B₁(α, δ) related to the Bernoulli Lemniscate function on the unit disk D = {z : |z| < 1} and obtain the upper bounds of the determinant H₂(1), H₂(2), T₂(1), and investigate H₂(1) using coefficients invers function. We used lemma from Charateodory-Toeplitz and Libera about sharp inequalities for functions with positive real part.

Original language	English
Pages (from-to)	1290-1301
Number of pages	12
Journal	European Journal of Pure and Applied Mathematics
Volume	16
Issue number	2
DOIs	https://doi.org/10.29020/nybg.ejpam.v16i2.4772
Publication status	Published - Apr 2023

Keywords

Bazilevič functions
Bernoulli Lemniscate
Coefficients
Hankel determinant
Subordination
Toeplitz determinant

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10.29020/nybg.ejpam.v16i2.4772

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title = "Hankel Determinant and Toeplitz Determinant on the Class of Bazilevi{\v c} Functions Related to the Bernoulli Lemniscate",

abstract = "In this papers, we investigate the Hankel determinant and Toeplitz determinant for the class Bazilevi{\v c} Function B1(α, δ) related to the Bernoulli Lemniscate function on the unit disk D = \{z : |z| < 1\} and obtain the upper bounds of the determinant H2(1), H2(2), T2(1), and investigate H2(1) using coefficients invers function. We used lemma from Charateodory-Toeplitz and Libera about sharp inequalities for functions with positive real part.",

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author = "Asih, \{Ni Made\} and Sa{\textquoteright}adatul Fitri and Wibowo, \{Ratno Bagus Edy\} and Marjono",

year = "2023",

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doi = "10.29020/nybg.ejpam.v16i2.4772",

language = "English",

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T1 - Hankel Determinant and Toeplitz Determinant on the Class of Bazilevič Functions Related to the Bernoulli Lemniscate

AU - Asih, Ni Made

AU - Fitri, Sa’adatul

AU - Wibowo, Ratno Bagus Edy

AU - Marjono,

PY - 2023/4

Y1 - 2023/4

N2 - In this papers, we investigate the Hankel determinant and Toeplitz determinant for the class Bazilevič Function B1(α, δ) related to the Bernoulli Lemniscate function on the unit disk D = {z : |z| < 1} and obtain the upper bounds of the determinant H2(1), H2(2), T2(1), and investigate H2(1) using coefficients invers function. We used lemma from Charateodory-Toeplitz and Libera about sharp inequalities for functions with positive real part.

AB - In this papers, we investigate the Hankel determinant and Toeplitz determinant for the class Bazilevič Function B1(α, δ) related to the Bernoulli Lemniscate function on the unit disk D = {z : |z| < 1} and obtain the upper bounds of the determinant H2(1), H2(2), T2(1), and investigate H2(1) using coefficients invers function. We used lemma from Charateodory-Toeplitz and Libera about sharp inequalities for functions with positive real part.

KW - Bazilevič functions

KW - Bernoulli Lemniscate

KW - Coefficients

KW - Hankel determinant

KW - Subordination

KW - Toeplitz determinant

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DO - 10.29020/nybg.ejpam.v16i2.4772

M3 - Article

AN - SCOPUS:85161518015

SN - 1307-5543

VL - 16

SP - 1290

EP - 1301

JO - European Journal of Pure and Applied Mathematics

JF - European Journal of Pure and Applied Mathematics

IS - 2

ER -

Hankel Determinant and Toeplitz Determinant on the Class of Bazilevič Functions Related to the Bernoulli Lemniscate

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Keywords

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