Abstract
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.
For A.McD. (Rex) Mercer, in loving memory.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
S.J. Karlin, W.J. Studden, Tchebychev Systems: With Applications in Analysis and Statistics (Interscience, New York, 1966)
V.I. Levin, S.B. Stečkin, Inequalities. Am. Math. Soc. Transl. 14, 1–29 (1960)
P.R. Mercer, A note on inequalities due to Clausing and Levin–Stečkin. J. Math. Inequal. 11, 163–166 (2017)
P.R. Mercer, A note on the Fejer and Levin–Stečkin inequalities. Anal. Math. 43, 99–102 (2017)
J. Pečarić, A. Ur Rehman, Cauchy means introduced by an inequality of Levin and Stečkin. East J. Approx. 15, 515–524 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mercer, P.R. (2019). The Levin–Stečkin Inequality and Simple Quadrature Rules. In: Andrica, D., Rassias, T. (eds) Differential and Integral Inequalities. Springer Optimization and Its Applications, vol 151. Springer, Cham. https://doi.org/10.1007/978-3-030-27407-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-27407-8_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27406-1
Online ISBN: 978-3-030-27407-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)