Geodesic
Approximation of the Stieltjes integral and applications in numerical integration
Applications of Mathematics, Tome 51 (2006) no. 1, pp. 37-47.

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Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.
DOI : 10.1007/s10492-006-0003-0
Classification : 26D15, 41A55, 65D30
Keywords: Stieltjes integral; quadrature rule; Fourier Sine transform; Fourier Cosine transform 
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Cerone, Pietro; Dragomir, Sever S. Approximation of the Stieltjes integral and applications in numerical integration. Applications of Mathematics, Tome 51 (2006) no. 1, pp. 37-47. doi : 10.1007/s10492-006-0003-0. http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0003-0/

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