The Levin–Stečkin Inequality and Simple Quadrature Rules

  • Peter R. MercerEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 151)


We obtain an error term for an extension of the Levin–Stečkin Inequality, which yields the error terms for the Midpoint, Trapezoid, and Simpson’s rules.


  1. 1.
    S.J. Karlin, W.J. Studden, Tchebychev Systems: With Applications in Analysis and Statistics (Interscience, New York, 1966)zbMATHGoogle Scholar
  2. 2.
    V.I. Levin, S.B. Stečkin, Inequalities. Am. Math. Soc. Transl. 14, 1–29 (1960)Google Scholar
  3. 3.
    P.R. Mercer, A note on inequalities due to Clausing and Levin–Stečkin. J. Math. Inequal. 11, 163–166 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    P.R. Mercer, A note on the Fejer and Levin–Stečkin inequalities. Anal. Math. 43, 99–102 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    J. Pečarić, A. Ur Rehman, Cauchy means introduced by an inequality of Levin and Stečkin. East J. Approx. 15, 515–524 (2009)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsSUNY College at BuffaloBuffaloUSA

Personalised recommendations