Previous |  Up |  Next


Stieltjes integral; quadrature rule; Fourier Sine transform; Fourier Cosine transform
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.
[1] P.  Cerone, S. S.  Dragomir: Midpoint-type rules from an inequalities point of view. In: Handbook of Analytic-Computational Methods in Applied Mathematics, G. A.  Anastassiou (ed.), CRC Press, 2000, pp. 135–200. MR 1769925
[2] P.  Cerone, S. S.  Dragomir: New bounds for the three-point rule involving the Riemann-Stieltjes integral. In: Advances in Statistics, Combinatorics and Related Areas, C.  Gulati et al. (eds.), World Scientific, London, 2002, pp. 53–62. MR 2063836
[3] P.  Cerone, S. S.  Dragomir: Approximation of the Stieltjes integral and applications in numerical integration. RGMIA Res. Rep. Coll. 6 (2003), Article 10 [Online:]
[4] S. S.  Dragomir: On the Ostrowski’s integral inequality for mappings with bounded variation and applications. Math. Inequal. Appl. 4 (2001), 59–66. MR 1809841 | Zbl 1016.26017
[5] S. S.  Dragomir, I.  Fedotov: An inequality of Grüss’ type for Riemann-Stieltjes integral and applications for special means. Tamkang J.  Math. 29 (1998), 286–292. MR 1648534
[6] S. S.  Dragomir, I.  Fedotov: A Grüss type inequality for mappings of bounded variation and applications to numerical analysis. Nonlinear Funct. Anal. Appl. 6 (2001), 425–438. MR 1875552
[7] S. S.  Dragomir, A.  Kalam: An approximation of the Fourier Sine transform via Grüss type inequalities and applications for electrical circuits. J.  KSIAM 6 (2002), 33–45.
[8] Ostrowski Type Inequalities and Applications in Numerical Integration. S. S.  Dragomir, Th. M.  Rassias (eds.), Kluwer Academic Publishers, Dordrecht-Boston-London, 2002. MR 1928290 | Zbl 0992.26002
[9] I. N.  Sneddon: Fourier Transforms. McGraw-Hill, New York-Toronto-London, 1987. MR 0041963
Partner of
EuDML logo