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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
연도 인용수 순위
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 A general Ostrowski type inequality for double integrals /
[ G. Hanna;S. S. Dragomir;P. Cerone ] / RGMIA Res. Rep. Coll.
7 Bounds on the derivation of a function from its averages /
[ A. M. Fink ] / Czechoslovak Math. J.
8 Three point quadrature rules involving, at most, a first derivative /
[ P. Cerone;S. S. Dragomir ] / RGMIA Res. Rep. Coll.
9 On relationships between Ostrowski, trapezoidal and Chebychev identities and inequalities /
[ P. Cerone ] / RGMIA Res. Rep. Coll.
10 On a new Ostrowski type inequality in two independent variables /
[ B. G. Pachpatte ] / Tamkang J. Math.
11 /
[ P. Cerone;S. S. Dragomir;G.A. Anastassiou(Ed) ] / Handbook of Analytic-Computational Methods in Applied Mathematics
12 On some integral inequalities /
[ G. V. Milovanic ] / Univ. Beograd. Publ. Elek. Fak., Ser. Mat. Fiz.
13 /
[ D. S. Mitrinovic;J. E. Pecaric;A. M. Fink ] / Classical and New Inequalities in Analysis
14 A generalised trapezoid inequality for functions of bounded variation /
[ P. Cerone;S. S. Dragomir;C. E. M. Pearce ] / Turkish J. Math.
15 Some Ostrowski type inequalities for n-time differentiable mappings and applications /
[ P. Cerone;S. S. Dragomir;J. Roumeliotis ] / Demonstratio 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 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)
22 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.
23 /
[ S. S. Dragomir(Ed.);T. M. Rassias(Ed.) ] / Ostrowski type inequalities and applications in numerical integration