P. Cerone, S. S. Dragomir, School of Computer Science and Mathematics, Victoria University, PO Box 14428, MCMC 8001, Victoria, Australia, e-mails: pc@csm.vu.edu.au, sever@csm.vu.edu.au
Abstract: 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.
Keywords: Stieltjes integral, quadrature rule, Fourier Sine transform, Fourier Cosine transform
Classification (MSC 2000): 26D15, 41A55
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