Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions

Deepak Kumar; Virendra Kumar; Laxminarayan Das

Applications of Mathematics (2023)

  • Volume: 68, Issue: 3, page 289-304
  • ISSN: 0862-7940

Abstract

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In this paper, we have determined the sharp lower and upper bounds on the fourth-order Hermitian-Toeplitz determinant for starlike functions with real coefficients. We also obtained the sharp bounds on the Hermitian-Toeplitz determinants of inverse and logarithmic coefficients for starlike functions with complex coefficients. Sharp bounds on the modulus of differences and difference of moduli of logarithmic and inverse coefficients are obtained. In our investigation, it has been found that the bound on the third-order Hermitian-Toeplitz determinant for starlike functions and its inverse coefficients is invariant.

How to cite

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Kumar, Deepak, Kumar, Virendra, and Das, Laxminarayan. "Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions." Applications of Mathematics 68.3 (2023): 289-304. <http://eudml.org/doc/299541>.

@article{Kumar2023,
abstract = {In this paper, we have determined the sharp lower and upper bounds on the fourth-order Hermitian-Toeplitz determinant for starlike functions with real coefficients. We also obtained the sharp bounds on the Hermitian-Toeplitz determinants of inverse and logarithmic coefficients for starlike functions with complex coefficients. Sharp bounds on the modulus of differences and difference of moduli of logarithmic and inverse coefficients are obtained. In our investigation, it has been found that the bound on the third-order Hermitian-Toeplitz determinant for starlike functions and its inverse coefficients is invariant.},
author = {Kumar, Deepak, Kumar, Virendra, Das, Laxminarayan},
journal = {Applications of Mathematics},
keywords = {starlike function; Hermitian-Toeplitz determinant; logarithmic coefficient; inverse coefficient},
language = {eng},
number = {3},
pages = {289-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions},
url = {http://eudml.org/doc/299541},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Kumar, Deepak
AU - Kumar, Virendra
AU - Das, Laxminarayan
TI - Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 289
EP - 304
AB - In this paper, we have determined the sharp lower and upper bounds on the fourth-order Hermitian-Toeplitz determinant for starlike functions with real coefficients. We also obtained the sharp bounds on the Hermitian-Toeplitz determinants of inverse and logarithmic coefficients for starlike functions with complex coefficients. Sharp bounds on the modulus of differences and difference of moduli of logarithmic and inverse coefficients are obtained. In our investigation, it has been found that the bound on the third-order Hermitian-Toeplitz determinant for starlike functions and its inverse coefficients is invariant.
LA - eng
KW - starlike function; Hermitian-Toeplitz determinant; logarithmic coefficient; inverse coefficient
UR - http://eudml.org/doc/299541
ER -

References

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