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Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions

Published online by Cambridge University Press:  17 April 2009

W.-S. Cheung
Affiliation:
Department of Mathematics, University of Hong Kong, Hong Kong, e-mail: wscheung@hku.hk
S. S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University, PO Box 14428, MCMC 8001, Victoria, Australia, e-mail: sever@csm.vu.edu.au
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Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

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