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On Extremal Properties of the Derivatives of Polynomials and Rational Functions

Published online by Cambridge University Press:  20 November 2018

M.A. Malik
M.A. Malik*
Affiliation:
Université de Montréal and Regional Engineering College, SrinagarIndia
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Let p(z) be a polynomial of degree n, i. e. a finite sum of the form where cν are any given numbers and z=x+iy is a complex variable. To answer a question raised by the chemist Mendelieff, A. Markoff [3] proved the following theorem.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 1 , March 1964 , pp. 121 - 131
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bernstein, S., Sur I' ordre de la meilleure approximation des fonctions continues par des polynomes de degré donné, Mémoires de l' Académie Royale de Belgique, (2), 4(1912), 1–103.Google Scholar
2. Erdős, P., On extremal properties of the derivative of the polynomials, Annals of Math. 41(1940), 310–313.Google Scholar
3. Markoff, A., On a certain problem of D.I. Mendelieff, Utcheniya Zapiski Imperatorskoi Akademie Nauk. (Russia) 62 (1889), 1–24.Google Scholar