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Approximation of the Stieltjes Integral and Applications in Numerical Integration

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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.

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Authors and Affiliations

  1. School of Computer Science and Mathematics, Victoria University, PO Box 14428, MCMC, 8001, Victoria, Australia

    Pietro Cerone & Sever S. Dragomir

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  1. Pietro Cerone
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  2. Sever S. Dragomir
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Cerone, P., Dragomir, S.S. Approximation of the Stieltjes Integral and Applications in Numerical Integration. Appl Math 51, 37–47 (2006). https://doi.org/10.1007/s10492-006-0003-0

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  • DOI: https://doi.org/10.1007/s10492-006-0003-0

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