Inequalities of Markoff and Bernstein

  • Q. I. Rahman
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)


In the early part of this century, de la Vallée Poussin raised the following question of best approximation: Is it possible to approximate every polygonal line by polynomials of degree n with an error of o(l/n) as n becomes large? The question was answered in the negative by S. Bernstein. For this he proved and made considerable use of an inequality concerning the derivatives of polynomials. This inequality and a related (and earlier) one by A.A. Markoff have been the starting point of a considerable literature. Here we discuss some of the investigations which have centered about these inequalities.


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Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Q. I. Rahman
    • 1
  1. 1.Department of MathematicsUniversity of MontrealMontrealCanada

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