ON THE ZERO-FREE REGIONS FOR POLAR DERIVATIVE OF POLYNOMIALS WITH RESTRICTED COEFFICIENTS
In this paper, we prove some extension results on the Eneström-Kakeya theorem and obtain some results on the zero-free regions for polar derivatives of polynomials with restricted coefficients.
zeros of polynomial, Eneström-Kakeya theorem, polar derivative.
Received: May 29, 2021; Accepted: July 23, 2021; Published: November 15, 2021
How to cite this article: C. Gangadhar, P. Ramulu, G. L. Reddy and P. Venkateshwarlu, On the zero-free regions for polar derivative of polynomials with restricted coefficients, Advances in Differential Equations and Control Processes 25(1) (2021), 127-139. DOI: 10.17654/DE025020127
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] A. Aziz and Q. G. Mohammad, Zero free regions for polynomials and some generalizations of Eneström-Kakeya theorem, Canad. Math. Bull. 27(3) (1984), 265-272.[2] K. K. Dewan and M. Bidkham, On the Eneström-Kakeya theorem, J. Math. Anal. Appl. 180 (1993), 29-36.[3] G. Eneström, Remarquee sur un théorème relatif aux racines de l’equation oü tous les coefficient sont et positifs, Tôhoku Math. J. 18 (1920), 34-36.[4] M. H. Gulzar, Zero-free regions for polynomials with restricted coefficients, International Journal of Engineering and Science 2(6) (2013), 6-10.[5] C. Gangadhar, P. Ramulu and G. L. Reddy, Zero-free regions for polar derivative of polynomials with restricted coefficients, Internat. J. Pure Engg. Math. (IJPEM) (to appear).[6] S. Kakeya, On the limits of the roots of an algebraic equation with positive coefficient, Tôhoku Math. J. 2 (1912-1913), 140-142.[7] P. Ramulu, Some generalization of Eneström-Kakeya theorem, International Journal of Mathematics and Statistics Invention 3(2) (2015), 52-59.[8] G. L. Reddy, P. Ramulu and C. Gangadhar, Zero-free region for polynomials with restricted coefficients, International Journal of Science and Research 4(4) (2015), 2937-2942.