THE BOUNDS FOR THE ZEROS OF POLYNOMIALS Transactions of A Razmadze Mathematical Institute, 2025
AN IMPROVEMENT OF CAUCHY RADIUS FOR THE ZEROS OF A POLYNOMIAL Subhasis Das Mathematica, 2023 "For a given polynomial p(z) =a_{n}z^{n}+a_{n-1}z^{n-1}+\cdots +a_{1}z+a_{0} of degree n with complex coefficients, the Cauchy radius r_{0} is a unique positive root of the equation |a_{n}| t^{n}-(|a_{n-1}|t^{n-1}+|a_{n-2}| t^{n-2}+ ... +|a_{1}| t+ |a_{0}|) =0. It refers to a radius of the circular region |z|<= r_{0} in which all the zeros of p(z) lie. The basic aim has been to determine the smallest radius, thereby, minimizing the area of the circular region. In this present paper, we have obtained a result which gives an improvement of the Cauchy radius. Also, we produce an annular region whose center is different from the origin in which the zeros of p(z) lie. Moreover, in many cases, our results give better approximations for estimating the region of polynomial zeros than that obtained from many other well-known results."
Location of zeros of a Lacunary type polynomial Subhasis Das and Annals of the University of Craiova Mathematics and Computer Science Series, 2022 For a given polynomial p(z) of degree n with real or complex coefficients, our basic aim has been to determine the smallest region in which all the zeros of p(z) lie. In the present paper, we have obtained a result by using Lacunary type polynomial which gives the region of zeros neither circular nor annular except in some particular cases. Our result plays an important role to reduce the region of polynomial zeros.
THE BOUNDS FOR THE ZEROS OF POLYNOMIALS. S DAS Transactions of A. Razmadze Mathematical Institute 179 (1) , 2025 2025
AN IMPROVEMENT OF CAUCHY RADIUS FOR THE ZEROS OF A POLYNOMIAL. S DAS Mathematica (1222-9016) 65 (2) , 2023 2023
Location of zeros of a Lacunary type polynomial S Das Annals of the University of Craiova-Mathematics and Computer Science Series … , 2022 2022
Zeros of Lacunary Type Polynomials S Das Eurasian Mathematical Journal 13 (1), 32-43 , 2022 2022
Annular bounds for the zeros of polynomials S Das Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie … , 2020 2020 Citations: 3
ON CAUCHY’S TYPE BOUND FOR ZEROS OF A POLYNOMIAL S Das ANNALS OF THE ACADEMY OF ROMANIAN SCIENTISTS: SERIES ON MATHEMATICS AND ITS … , 2020 2020
On zeros of polynomial S Das Уфимский математический журнал 11 (1), 113-119 , 2019 2019 Citations: 1
On Cauchy’s proper bound for zeros of a polynomial S Das, SK Datta Int. J. Math. Sci. Eng. Apple 2 (4), 241-252 , 2008 2008 Citations: 8
Certain generalizations of Eneström-Kakeya theorem A Chattopadhyay, S Das, VK Jain, H Konwer J. Indian Math. Soc 72 (1-4), 147-156 , 2005 2005 Citations: 19
MOST CITED SCHOLAR PUBLICATIONS
Certain generalizations of Eneström-Kakeya theorem A Chattopadhyay, S Das, VK Jain, H Konwer J. Indian Math. Soc 72 (1-4), 147-156 , 2005 2005 Citations: 19
On Cauchy’s proper bound for zeros of a polynomial S Das, SK Datta Int. J. Math. Sci. Eng. Apple 2 (4), 241-252 , 2008 2008 Citations: 8
Annular bounds for the zeros of polynomials S Das Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie … , 2020 2020 Citations: 3
On zeros of polynomial S Das Уфимский математический журнал 11 (1), 113-119 , 2019 2019 Citations: 1
THE BOUNDS FOR THE ZEROS OF POLYNOMIALS. S DAS Transactions of A. Razmadze Mathematical Institute 179 (1) , 2025 2025
AN IMPROVEMENT OF CAUCHY RADIUS FOR THE ZEROS OF A POLYNOMIAL. S DAS Mathematica (1222-9016) 65 (2) , 2023 2023
Location of zeros of a Lacunary type polynomial S Das Annals of the University of Craiova-Mathematics and Computer Science Series … , 2022 2022
Zeros of Lacunary Type Polynomials S Das Eurasian Mathematical Journal 13 (1), 32-43 , 2022 2022
ON CAUCHY’S TYPE BOUND FOR ZEROS OF A POLYNOMIAL S Das ANNALS OF THE ACADEMY OF ROMANIAN SCIENTISTS: SERIES ON MATHEMATICS AND ITS … , 2020 2020
