Quadrature formulas with variable nodes and Jackson–Nikolskii inequalities for rational functions

Petr Chunaev, Vladimir Danchenko

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1 Citation (Scopus)

Abstract

© 2018 Elsevier Inc. We obtain new parametric quadrature formulas with variable nodes for integrals of complex rational functions over circles, segments of the real axis and the real axis itself. Basing on these formulas we derive (q,p)-inequalities of Jackson–Nikolskii type for various classes of rational functions, complex polynomials and their logarithmic derivatives (simple partial fractions). It is shown that our (∞,2)- and (∞,4)-inequalities are sharp in a number of main theorems. Our inequalities extend and refine several results obtained earlier by other authors.
Original languageEnglish
Pages (from-to)1-20
JournalJournal of Approximation Theory
Volume228
DOIs
Publication statusPublished - 1 Apr 2018

Keywords

  • Jackson–Nikolskii inequalities
  • Quadrature formulas
  • Rational functions

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