Browse > Article
http://dx.doi.org/10.4134/CKMS.c170466

ON THE MAXIMUM AND MINIMUM MODULUS OF POLYNOMIALS ON CIRCLES  

Chong, Han Kyol (Jinjujeil High School)
Kim, Seon-Hong (Department of Mathematics Sookmyung Women's University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.4, 2018 , pp. 1303-1308 More about this Journal
Abstract
In this paper, we consider both maximum modulus and minimum modulus on a circle of some polynomials. These give rise to interesting examples that are about moduli of Chebyshev polynomials and certain sums of polynomials on a circle. Moreover, we obtain some root locations of difference quotients of Chebyshev polynomials.
Keywords
modulus; polynomials; difference quotients; Chebyshev polynomials;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 H. J. Fell, On the zeros of convex combinations of polynomials, Pacific J. Math. 89 (1980), no. 1, 43-50.   DOI
2 N. K. Govil, On the maximum modulus of polynomials, J. Math. Anal. Appl. 112 (1985), no. 1, 253-258.   DOI
3 S.-H. Kim, Sums of two polynomials with each having real zeros symmetric with the other, Proc. Indian Acad. Sci. Math. Sci. 112 (2002), no. 2, 283-288.   DOI
4 S.-H. Kim and J. H. Lee, On difference quotients of Chebyshev polynomials, Bull. Korean Math. Soc. 53 (2016), no. 2, 373-386.   DOI
5 M. A. Qazi, On the maximum modulus of polynomials, Proc. Amer. Math. Soc. 115 (1992), no. 2, 337-343.   DOI
6 Q. I. Rahman and G. Schmeisser, Analytic Theory of Polynomials, London Mathematical Society Monographs. New Series, 26, The Clarendon Press, Oxford University Press, Oxford, 2002.
7 T. J. Rivlin, On the maximum modulus of polynomials, Amer. Math. Monthly 67 (1960), 251-253.   DOI