Sharp inequality of three point Gauss-Legendre quadrature rule
Keywords:Gauss quadrature formula, Holder inequality
An interesting identity for 3-point Gauss-Legendre quadrature rule using functions that are n-times differentiable. By applying the established identity, a sharp inequality which gives an error bound for 3-point Gauss-Legendre quadrature rule and some generalizations are derived. At the end, an application in numerical integration is given.
M. W. Alomari and A. Guessab, “Lp –error bounds of two and three–point quadrature rules for Riemann–Stieltjes integrals”, Moroccan journal of pure and applied analysis, vol. 4, no. 1, pp. 33–43, Jun. 2018, doi: 10.1515/mjpaa-2018-0004
M. W. Alomari, “Two-point Ostrowski’s inequality”, Results in mathematics, vol. 72, no. 3, pp. 1499–1523, Jul. 2017, doi: 10.1007/s00025-017-0720-6
M. W. Alomari, “New Sharp Ostrowski-type inequalities and generalized trapezoid-type inequalities for Riemann–Stieltjes integrals and their applications”, Ukrainian mathematical journal, vol. 65, no. 7, pp. 995–1018, Dec. 2013, doi: 10.1007/s11253-013-0837-z
P. Cerone and S. S. Dragomir, “New bounds for the three—point rule involving the Riemann—Stieltjes integrals”, in Advances in statistics, combinatorics and related areas, C. Gulati , Y.-X. Lin, S. Mishra, and J. Rayner, Eds. World Scientific, 2002, pp. 53–62, doi: 10.1142/9789812776372_0006
S. S. Dragomir, “Approximating the Riemann–Stieltjes integral by a trapezoidal quadrature rule with applications”, Mathematical and computer modelling, vol. 54, no. 1-2, pp. 243–260, Jul. 2011., doi: 10.1016/j.mcm.2011.02.006
A. Guessab and G. Schmeisser, “Sharp integral inequalities of the Hermite–Hadamard type”, Journal of approximation theory, vol. 115, no. 2, pp. 260–288, Apr. 2002, doi: 10.1006/jath.2001.3658
M. Tortorella, “Closed Newton–Cotes quadrature rules for Stieltjes integrals and numerical convolution of life distributions”, SIAM journal on scientific and statistical computing, vol. 11, no. 4, pp. 732–748, Jul. 1990, doi: 10.1137/0911043
N. Ujević, “Two sharp Ostrowski—like inequalities and applications”, Methods and applications of analysis, vol. 10, no. 3, pp. 477-486, 2003. [On line]. Available: https://bit.ly/2TP2zaO
N. Ujević, “N. Two sharp inequalities of Simpson type and applications”, Georgian mathematical journal, vol. 11, no. 1, pp. 187-194, 2004. [On line]. Available: https://bit.ly/3gy3MNJ
N. Ujević and L. Mijić, “An optimal 3—point quadrature formula of closed type and error bounds”, Revista colombiana de matemáticas, vol. 42, no. 2, pp. 209-220, 2008. [On line]. Available: https://bit.ly/2M7VONm
M. W. Alomari, “Two point Gauss—Legendre quadrature rule for Riemann—Stieltjes integrals”, Feb. 2014, arXiv: 1402.4982v1
F. Zafar and N. Mir, “Some generalized error inequalities and applications”, Journal of inequalities and applications, vol. 2008, no. 1, Art ID. 845934, 2008, doi: 10.1155/2008/845934
How to Cite
Copyright (c) 2020 Artion Kashuri
This work is licensed under a Creative Commons Attribution 4.0 International License.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.