Abstract
Upper and lower error bounds for an optimal 2-point quadrature rule of open type are derived. These error bounds are sharp. Applications in numerical integration are given
Similar content being viewed by others
References
P. Cerone, Three points rules in numerical integration, Nonlinear Anal.-Theory Methods Appl. 47 (4), (2001), 2341–2352.
S. S. Dragomir, R. P. Agarwal and P. Cerone, On Simpson's inequality and applications, J. Inequal. Appl. 5 (2000), 533–579.
P. Cerone and S. S. Dragomir, Midpoint-type rules from an inequalities point of view, Handbook of analytic-computational methods in applied mathematics, ed. By G. Anastassiou, CRC Press, New York, 2000, 135–200.
P. Cerone and S. S. Dragomir, Trapezoidal-type rules from an inequalities point of view, Handbook of analytic-computational methods in applied mathematics, ed. by G. Anastassiou, CRC Press, New York, 2000, 65–134.
S. S. Dragomir, P. Cerone and J. Roumeliotis, A new generalization of Os-trowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett. 13 (2000), 19–25.
S. S. Dragomir, J. PeČariĆ and S. Wang, The unified treatment of trapezoid, Simpson and Ostrowski type inequalities for monotonic mappings and applications, Math. Comput. Modelling 31 (2000), 61–70.
A. Ghizzetti and A. Ossicini, Quadrature formulae, Birkhauser Verlag, Basel–Stuttgart, 1970.
A. R. Krommer and C. W. Ueberhuber, Computational integration, SIAM, Philadelphia, 1998.
D. S. MitrinoviĆ, J. PeČariĆ and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Acad. Publ., Dordrecht, 1991.
C. E. M. Pearce, J. PeČariĆ, N. UjeviĆ and S. VaroŠanec, Generalizations of some inequalities of Ostrowski-Grüss type, Math. Inequal. Appl. 3 (1) (2000), 25–34.
N. UjeviĆ, Inequalities of Ostrowski-Grüss type and applications, Appl. Math. 29 (4) (2002), 465–479.
N. UjeviĆ, Some double integral inequalities and applications, Acta Math. Univ. Comenianae 71, 2 (2002), 189–199. [13] N.UJEVI C, An optimal quadrature formula of open type, (submitted).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ujević, N. Double integral inequalities and application in numerical integration. Periodica Mathematica Hungarica 49, 141–149 (2004). https://doi.org/10.1023/B:MAHU.0000040545.96525.86
Issue Date:
DOI: https://doi.org/10.1023/B:MAHU.0000040545.96525.86