Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On a polynomial inequality of E. J. Remez


Authors: D. Dryanov and Q. I. Rahman
Journal: Proc. Amer. Math. Soc. 128 (2000), 1063-1070
MSC (1991): Primary 30A10, 30C10, 41A17
DOI: https://doi.org/10.1090/S0002-9939-99-05092-3
Published electronically: July 27, 1999
MathSciNet review: 1636946
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a result which extends a well-known polynomial inequality of E. J. Remez and another one due to W. A. Markov.


References [Enhancements On Off] (What's this?)

  • 1. B. Bojanov, Elementary Proof of the Remez Inequality, Amer. Math. Monthly 100 (1993), pp. 1-99. CMP 93:11
  • 2. P. Borwein & T. Erdélyi, Polynomials and Polynomial Inequalities, Springer - Verlag, 1995. MR 97e:41001
  • 3. G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1971.
  • 4. E. Hille, Analytic Function Theory, vol. I, Blaisdel Publishing Company , New York, 1959. MR 21:6415
  • 5. V.A. Markov (W.A. Markov), Über polynôme die in einem gegebenem Intervalle möglichst wenig von Null abweichen, Math. Ann. 77 (1916), pp. 1-99.
  • 6. G. V. Milovanovi\'{c}, D. S. Mitrinovi\'{c}, Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, World Scientific, Singapore, 1994. MR 95m:30009
  • 7. I.P. Natanson, Constructive Function Theory, vol. I, Frederick Ungar Publishing Co., Inc., New York, 1964. MR 33:4529a
  • 8. E.J. Remez, Sur une propriété des polynômes de Tchebycheff, Comm. Inst. Sci. Khar-kow 13 (1936), pp. 1-99.
  • 9. T.J. Rivlin, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, 2nd ed., Wiley & Sons, New York, 1990.MR 92a:41016

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30A10, 30C10, 41A17

Retrieve articles in all journals with MSC (1991): 30A10, 30C10, 41A17


Additional Information

D. Dryanov
Affiliation: Department of Mathematics, University of Sofia, James Boucher 5, 1126 Sofia, Bulgaria
Email: dryanovd@fmi.uni-sofia.bg

Q. I. Rahman
Affiliation: Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Canada H3C 3J7
Email: rahmanqi@ere.umontreal.ca

DOI: https://doi.org/10.1090/S0002-9939-99-05092-3
Keywords: Polynomials, Markov's inequality, Remez inequality
Received by editor(s): May 12, 1997
Received by editor(s) in revised form: May 25, 1998
Published electronically: July 27, 1999
Additional Notes: The first author was partially supported by the Bulgarian Ministry of Education, Sciences, and Technology through Contract 513/95.
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society