On simpson's inequality and applications

Journal of Inequalities and Applications

Volumn 5, Issue 6, 2000, Pages 533-579

  Dragomir, S S ^a   Agarwal, R R ^a   Cerone, P ^a,b  

^a VICTORIA UNIVERSITY   (Australia)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Quadrature formulae; Simpson's inequality

Indexed keywords

EID: 0000050032     PISSN: 10255834     EISSN: 1029242X     Source Type: Journal    
DOI: 10.1155/S102558340000031X     Document Type: Article

References (32)

1. D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
2. S. S. Dragomir, On Simpson's quadrature formula for mappings of bounded variation and applications, Tamkang J. Mathematics, 30 (1) (1999), 53-58.
3. S. S. Dragomir, On Simpson's quadrature formula for Lipschitzian mappings and applications, Soochow J. Mathematics, 25 (2) (1999), 175-180.
4. p spaces and applications, J. KSIAM, 2 (2) (1998), 57-65.
5. D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
6. S. S. Dragomir and S. Wang, An inequality of Ostrowski-Grüss' type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. Applic., 33(1997), 15-20. (Pubitemid 127382554)
7. 1 norm and applications to some special means and to some numerical quadrature rules, Tamkang J. Mathematics, 28(1997), 239-244. (Pubitemid 128003024)
8. S. S. Dragomir and S. Wang, Applications of Ostrowski's inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl. Math. Lett, 11(1998), 105-109.
9. p norm, Indian J. Mathematics, 40 (3) (1998), 299-304.
10. P. Cerone, S. S. Dragomir and J. Rouumeliotis, An inequality of Ostrowski-Grüss type for twice diferentiable mappings and applications in numerical integration, Kyungpook Math. J. (in press).
11. N. S. Barnett and S. S. Dragomir, An inequality of Ostrowski's type for cumulative distribution functions, Kyungpook Math. J. (in press).
12. p-norms and applications in numerical integration, Rev. D'Analy. Num. Theor. Approx. (in press).
13. T. Peachey, A. Mc Andrew and S. S. Dragomir, The best constant in an equality of Ostrowski type, Tamkang J. Math., 30 (3) (1999), 219-222.
14. S. S. Dragomir, Y. J. Cho and S. S. Kim, Some remarks on Milanović-Pečarić inequality and applications for special means and numerical integration, Tamkang J. Math., 30 (3) (1999), 203-211.
15. S. S. Dragomir, R. P. Agarwal and N. S. Barnett, Inequalities for Beta and Gamma functions via some classical and new integral inequalities, Journal of Inequalities and Applications (accepted).
16. S. S. Dragomir, A generalization of Ostrowski integral inequality for mappings of bounded variation and applications in numerical integration, Bull. Australian Math. Soc., 60 (3) (1999), 495-508.
17. p>1, Mathematical Inequalities and Applications, 2 (4) (1999), 501-508.
18. S. S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, The Journal of the Indian Mathematical Society (accepted).
19. S. S. Dragomir, P. Cerone and J. Roumeliotis, A new generalization of Ostrowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett. (accepted).
20. S. S. Dragomir, Ostrowski's inequality for monotonic mappings and applications, J. KSIAM, 3 (2) (1999), 127-135.
21. I. Fedotov and S. S. Dragomir, An inequality of Ostrowski type and its applications for Simpson's rule and special means, Preprint, RGMIA Res. Rep. Coll., 2 (1) (1999), 13-20. http://matilda.vu.edu.au/~rgmia.
22. S. S. Dragomir, On the Ostrowski's integral inequality for mappings with bounded variation and applications, Preprint, RGMIA Research Report Collection, 2 (1) (1999), 63-70.
23. S. S. Dragomir, P. Cerone, J. Roumeliotis and S. Wang, A weighted version of Ostrowski inequality for mappings of Holder type and applications in numerical analysis, Preprint, RGMIA Research Report Collection, 2 (1) (1999), 95-104.
24. p (a, b) and applications, Preprint, RGMIA Research Report Collection, 1 (1) (1998), 41-50.
25. N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality for double integrals and applications for embouchure formulae, Preprint, RGMIA Research Report Collection, 1 (1) (1998), 13-22.
26. J. Roumeliotis, P. Cerone and S. S. Dragomir, An Ostrowski type inequality for weighted mappings with bounded second derivatives, Preprint, RGMIA Research Report Collection, 1 (1) (1998), 95-104.
27. ∞ and applications in numerical integration (submitted).
28. P. Cerone and S. S. Dragomir, On a weighted generalization of Iyengar type inequalities involving bounded first derivative, Math. Surg. Appl. (accepted).
29. S. S. Dragomir, N. S. Barnett and P. Cerone, An N-dimensional version of Ostrowski's inequality for mappings of the Holder type, Kyungpook. Math. J. (accepted).
30. 1[a, b] and applications in numerical integration, J. of Comp. Aerol. Appl. (accepted).
31. p[a, b] and applications in numerical integration (submitted).
32. S. S. Dragomir, J. E. Pečarić and S. Wang, The unified treatment of trapezoid, Simpson and Ostrowski type inequalities for monotonic mappings and applications, Mathematical and Computer Modelling (in press).