Geodesic
Error inequalities for some new quadrature formulas with weight involving $n$ knots and the $L_p$-norm of the $m$-th derivative on time scales
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 9-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we generalize the Ostrowski inequality on time scales for $n$ points and the $L_p$ norm of $m$-th derivative, where $m,n\in\mathbb N$ and $p\in[1,+\infty]$. 
@article{VMJ_2014_16_3_a1,
     author = {P. T. Dung and N. T. Chung and V. N. Huy},
     title = {Error inequalities for some new quadrature formulas with weight involving~$n$ knots and the $L_p$-norm of the $m$-th derivative on time scales},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {9--21},
     year = {2014},
     volume = {16},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a1/}
}
TY  - JOUR
AU  - P. T. Dung
AU  - N. T. Chung
AU  - V. N. Huy
TI  - Error inequalities for some new quadrature formulas with weight involving $n$ knots and the $L_p$-norm of the $m$-th derivative on time scales
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2014
SP  - 9
EP  - 21
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a1/
LA  - en
ID  - VMJ_2014_16_3_a1
ER  - 
%0 Journal Article
%A P. T. Dung
%A N. T. Chung
%A V. N. Huy
%T Error inequalities for some new quadrature formulas with weight involving $n$ knots and the $L_p$-norm of the $m$-th derivative on time scales
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 9-21
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a1/
%G en
%F VMJ_2014_16_3_a1
P. T. Dung; N. T. Chung; V. N. Huy. Error inequalities for some new quadrature formulas with weight involving $n$ knots and the $L_p$-norm of the $m$-th derivative on time scales. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 9-21. http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a1/

[1] Anastassiou G. A., Dragomir S. S., “On some estimates of the remainder in Taylor's formula”, J. Math. Anal. Appl., 263 (2001), 246–263 | DOI | MR | Zbl

[2] Bohner M., Mathtthewa T., “Ostrowski inequalities on time scales”, J. Inequal. Pure Appl. Math., 9:1 (2008), Article 6, 8 pp. | MR

[3] Bohner M., Mathtthewa T., “The Grüss inequality on time scales”, Commun. Math. Anal., 3:1 (2007), 1–8 | MR | Zbl

[4] Dragomir S. S., Wang S., “An inequality of Ostrowski Grüss's type and its applications to the astimation of error bounds for some special means and for some numercial quadrature rules”, Comput. Math. Appl., 33 (1997), 15–20 | DOI | MR | Zbl

[5] Huy V. N., Ngo Q. A., “New inequalities of Ostrowski-like type involving $n$ knots and the $L_p$-norm of the $m$-th derivative”, Appl. Math. Lett., 22 (2009), 1345–1350 | DOI | MR | Zbl

[6] Huy V. N., Ngo Q. A., “A new way to think about Ostrowski-like type inequalities”, Comput. Math. Appl., 59 (2010), 3045–3052 | DOI | MR | Zbl

[7] Huy V. N., Ngo Q. A., “New inequalities of Simpson-like type involving $k$ nots and the $m$-th derivative”, Math. Comput. Modelling, 52 (2010), 522–528 | DOI | MR | Zbl

[8] Hilger S., Ein Ma$\beta$kettenkalkul mit Anwendung auf Zentrmsmannigfaltingkeiten, PhD thesis, Univarsi. Wrzburg, 1988 | Zbl

[9] Matić M., “Improvement of some inequalities of Euler–Grüss type”, Comput. Math. Appl., 46 (2003), 1325–1336 | DOI | MR | Zbl

[10] Liu W., Ngo Q. A., “A generalization of Ostrowski inequality on time scales for $k$ points”, Appl. Math. Comput., 203:2 (2008), 754–760 | DOI | MR | Zbl

[11] Ostrowski A. M., “Uber die absolutabweichung einer differentiebaren funktion vom ihrem integralmitelwert”, Comment. Math. Helv., 10 (1938), 226–227 | DOI | MR | Zbl

[12] Ujević N., “Error inequalities for a quadrature formula of open type”, Rev. Colombiana Mat., 37 (2003), 93–105 | MR | Zbl

[13] Ujević N., “Error inequalities for a quadrature formula and applications”, Comput. Math. Appl., 48 (2004), 1531–1540 | DOI | MR | Zbl

[14] Ujević N., “New error bounds for the Simpsons quadrature rule and applications”, Comput. Math. Appl., 53 (2007), 64–72 | DOI | MR | Zbl

[15] Ujević N., “Sharp inequality of Simpson type and Ostrowski type”, Comput. Math. Appl., 48 (2004), 145–151 | DOI | MR | Zbl

[16] Nikol'ski S. M., Quadrature formulas, Nauka, M., 1974, 224 pp. (in Russian) | MR

[17] Krylov V. I., Approximating computation of integrals, Nauka, M., 1967, 500 pp. (in Russian) | MR

[18] Bernstein S. N., “About Cotes's and Chebyshev's quadrature formulas”, Collection of theses, v. 2, Nauka, M., 1954, 200–204 (in Russian)

[19] Bernstein S. N., “About one system of undefined equations”, Collection of theses, v. 2, Nauka, M., 1954, 236–242