Approximating the Stieltjes integral via a weighted trapezoidal rule with applications

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Article ID:	iaor20128596
Volume:	57
Issue:	3-4
Start Page Number:	602
End Page Number:	611
Publication Date:	Feb 2013
Journal:	Mathematical and Computer Modelling
Authors:	Dragomir S S, Fedotov I
Keywords:	Hilbert space

Abstract:

In this paper we provide sharp error bounds in approximating the weighted Riemann–Stieltjes integral $\int_{a}^{b} f (t) g (t) d a (t)$ equ1 by the weighted trapezoidal rule $\frac{f (a) + f (b)}{2} \int_{a}^{b} g (t) d a (t)$ equ2 . Applications for continuous functions of selfadjoint operators in complex Hilbert spaces are given as well.

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