A Note on Comparison of Annuli Containing all the Zeros of a Polynomial


Download PDF

Authors: S. HANS, A. TOMAR AND J. CHEN

DOI: 10.46793/KgJMat2201.139H

Abstract:



Keywords:

Polynomial, zeros, Fibonacci’s numbers.



References:

[1]   C. Affane-Aji, S. Biaz and N. K. Govil, On annuli containing all the zeros of a polynomial, Math. Comp. Modelling 52 (2010) 1532–1537.

[2]   A. Aziz and A. Qayoom, Estimates for the modulii of the zeros of a polynomial, Math. Inequal. Appl. 9 (2006) 107–116.

[3]   M. Bidkham and E. Shashahani, An annulus for the zeros of polynomials, Appl. Math. Lett. 24 (2011) 122–125.

[4]   A. L. Cauchy, Exercises de Mathématiques, IV, Anné de Bure Fréres, Paris, 1829.

[5]   A. Dalal and N. K. Govil, On region containing all the zeros of a polynomial, Appl. Math. Comput. 219 (2013) 9609–9614.

[6]   A. Dalal and N. K. Govil, Annulus containing all the zeros of a polynomial, Appl. Math. Comput. 249 (2014) 429–435.

[7]   A. Dalal and N. K. Govil, On comparison of annuli containing all the zeros of a polynomial, Appl. Anal. Discrete Math. 11 (2017) 232–241.

[8]   B. Datt and N. K. Govil, On the location of zeros of a polynomial, J. Approx. Theory 24 (1978) 78–82.

[9]   J. L. Diaz-Barrero, An annulus for the zeros of polynomials, J. Math. Anal. Appl. 273 (2002) 349–352.

[10]   J. L. Diaz-Barrero and J. J. Egozcue, Bounds for the moduli of zeros, Appl. Math. Lett. 17 (2004) 993–996.

[11]   A. Joyal, G. Labelle and Q. I. Rahman, On the location of zeros of polynomials, Canad. Math. Bull. 10 (1967) 53–63.

[12]   S. H. Kim, On the moduli of the zeros of a polynomial, Amer. Math. Monthly 112 (2005) 924–925.

[13]    M. Marden, Geometry of Polynomials, 2nd edition, Mathematical Surveys 3, Amer. Math. Soc. Providence, RI, USA, 1966.

[14]   G. V. Milovanović, D. S. Mitrinović and Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities and Zeros, World Scientific, Singapore, 1994.

[15]   Q. I. Rahman and G. Schmeisser, Analytic Theory of Polynomials, Oxford University Press Inc., New York, 2002.

[16]   Y. J. Sun and J. G. Hsieh, A note on circular bound of polynomial zeros, IEEE Trans. Circuits Syst. I. Regul. Pap. 43 (1996) 476–478.