Open Access Research

Sharp error bounds in approximating the Riemann-Stieltjes integral by a generalised trapezoid formula and applications

Pietro Cerone1* and Sever S Dragomir23

Author Affiliations

1 Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC, 3086, Australia

2 Mathematics, College of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne, MC, 8001, Australia

3 School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, Wits, 2050, South Africa

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Journal of Inequalities and Applications 2013, 2013:53  doi:10.1186/1029-242X-2013-53

Published: 18 February 2013

Abstract

Sharp error bounds in approximating the Riemann-Stieltjes integral <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/53/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/53/mathml/M1">View MathML</a> with the generalised trapezoid formula <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/53/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/53/mathml/M2">View MathML</a> are given for various pairs <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/53/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/53/mathml/M3">View MathML</a> of functions. Applications for weighted integrals are also provided.

MSC: 26D15, 26D10, 41A55.

Keywords:
Riemann-Stieltjes integral; trapezoid rule; integral inequalities; weighted integrals