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APPROXIMATING THE STIELTJES INTEGRAL OF BOUNDED FUNCTIONS AND APPLICATIONS FOR THREE POINT QUADRATURE RULES

  • Published : 2007.08.31

Abstract

Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.

Keywords

References

  1. Pietro Cerone and S. S. Dragomir, Three point identities and inequalities for n-time differentiable functions, SUT J. Math. 36 (2000), no. 2, 351-383
  2. Pietro Cerone and S. S. Dragomir, Approximation of the Stieltjes integral and applications in numerical integration, Appl. Math. 51 (2006), no. 1, 37-47 https://doi.org/10.1007/s10492-006-0003-0
  3. Pietro Cerone, S. S. Dragomir, and J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Math. 32 (1999), no. 4, 697-712
  4. Pietro Cerone, S. S. Dragomir, J. Roumeliotis, and J. Sunde, A new generalization of the trapezoid formula for n-time differentiable mappings and applications, Demonstratio Math. 33 (2000), no. 4, 719-736
  5. S. S. Dragomir, Inequalities of Gruss type for the Stieltjes integral and applications, Kragujevac J. Math. 26 (2004), 89-122
  6. S. S. Dragomir, A generalisation of Cerone's identity and applications, Tamsui Oxford J. Math. Sci. 23 (2007), No. 1, 79-90, Preprint RGMIA Res. Rep. Coll. 8 (2005), No. 2. Artcile 19
  7. S. S. Dragomir, Inequalities for Stieltjes integrals with convex integrators and applications, Appl. Math. Lett. 20 (2007), no. 2, 123-130 https://doi.org/10.1016/j.aml.2006.02.027
  8. S. S. Dragomir and I. Fedotov, An inequality of GrAuss' type for Riemann-Stieltjes inte- gral and applications for special means, Tamkang J. Math. 29 (1998), no. 4, 287-292
  9. S. S. Dragomir and I. Fedotov, A Gruss type inequality for mappings of bounded variation and applications to numerical analysis, Nonlinear Funct. Anal. Appl. 6 (2001), no. 3, 425-438
  10. S. S. Dragomir and Th. M. Rassias(Eds.), Ostrowski type inequalities and applications in numerical integration, Kluwer Academic Publishers, Dordrecht, 2002

Cited by

  1. A three point quadrature rule for functions of bounded variation and applications vol.57, pp.3-4, 2013, https://doi.org/10.1016/j.mcm.2012.07.024