[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2003.40.2.251

MULTIDIMENSIONAL INTEGRATION VIA TRAPEZOIDAL AND THREE POINT GENERATORS

Cerone, P. (School of Computer Science and Mathematics Victoria University of Technology)

Publication Information

Journal of the Korean Mathematical Society / v.40, no.2, 2003 , pp. 251-272 More about this Journal

Abstract

Multidimensional integrals are expressed in terms of lower dimensional integrals and function evaluations. An iterative process is used where a trapezoidal and three point identities are used as generators for higher dimensional identities. Bounds are obtained utilising the resulting identities. It is demonstrated that earlier Ostrowski type results are obtained as particular instances of the current work.

Keywords

multidimensional integrals; dimensional reduction; recursive method; generalised trapezoidal and three point generators.;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference
Cited By SCOPUS

1	An inequality of the Ostrowski type for double integrals and applications to cubature formulae / [ S. S. Dragomir;P. Cerone;N. S. Barnett;J. Roumeliotis ] / Tamsui Oxf. J. Math. Sci.
2	On some inequalities arising from Montgomery’s identity / [ P. Cerone;S. S. Dragomir ] / J. Compt. Anal. Appl.
3	Gruss’ inequality for positive linear functionals / [ D. Andrica;C. Badea ] / Period. Math. Hungar. DOI
4	Approximate multidimensional integration through dimension reduction via the Ostrowski functional / [ P. Cerone ] / RGMIA Research Report Collection
5	On an inequality of Ostrowski type in three independent variables / [ B. G. Pachpatte ] / J. Math. Anal. Appl. DOI ScienceOn
6	On relationships between Ostrowski, trapezoidal and Chebychev identities and inequalities / [ P. Cerone ] / RGMIA Res. Rep. Coll.
7	A general Ostrowski type inequality for double integrals / [ G. Hanna;S. S. Dragomir;P. Cerone ] / RGMIA Res. Rep. Coll.
8	Bounds on the derivation of a function from its averages / [ A. M. Fink ] / Czechoslovak Math. J.
9	Three point quadrature rules involving, at most, a first derivative / [ P. Cerone;S. S. Dragomir ] / RGMIA Res. Rep. Coll.
10	On a new Ostrowski type inequality in two independent variables / [ B. G. Pachpatte ] / Tamkang J. Math.
11	Some Ostrowski type inequalities for n-time differentiable mappings and applications / [ P. Cerone;S. S. Dragomir;J. Roumeliotis ] / Demonstratio Math.
12	/ [ P. Cerone;S. S. Dragomir;G.A. Anastassiou(Ed) ] / Handbook of Analytic-Computational Methods in Applied Mathematics
13	On some integral inequalities / [ G. V. Milovanic ] / Univ. Beograd. Publ. Elek. Fak., Ser. Mat. Fiz.
14	/ [ D. S. Mitrinovic;J. E. Pecaric;A. M. Fink ] / Classical and New Inequalities in Analysis
15	A generalised trapezoid inequality for functions of bounded variation / [ P. Cerone;S. S. Dragomir;C. E. M. Pearce ] / Turkish J. Math.
16	An Ostrowski type inequality for double integrals and applications for cubature formulae / [ N. S. Barnett;S. S. Dragomir ] / Soochow J. Math.
17	A trapezoid type inequality for double integrals / [ N. S. Barnett;S. S. Dragomir ] / RGMIA Research Report Collection
18	Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert / [ A. Ostrowski ] / Comment. Math. Helv. DOI
19	Ostrowski type inequalities / [ G. A. Anastassiou ] / Proc. Amer. Math. Soc. DOI ScienceOn
20	An Ostrowski type inequality in two dimensions using the three point rule / [ G. Hanna;P. Cerone;J. Roumeliotis ] / ANZIAM
21	/ [ S. S. Dragomir(Ed.);T. M. Rassias(Ed.) ] / Ostrowski type inequalities and applications in numerical integration
22	An Ostrowski type inequality for double integrals in terms of Lp-norms and applications in numerical integration / [ S. S. Dragomir;N. S. Barnett;P. Cerone ] / Anal. Num. Theor. Approx. (Romania)
23	A new generalisation of the trapezoidal formula for n-time differentiable mappings and applications / [ P. Cerone;S. S. Dragomir;J. Roumeliotis;J. Sunde ] / Demonstratio Math.