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Sharp bounds of Čebyšev functional for Stieltjes integrals and applications

Published online by Cambridge University Press:  17 April 2009

S. S. Dragomir
S. S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University of Technology, P.O. Box 14428, MCMC 8001, Vic.Australia e-mail: sever@matilda.vu.edu.au urladdr: http://rgmia.vu.edu.au/SSDragomirWeb.html
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Abstract

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Sharp bounds of the Čebyšev functional for the Stieltjes integrals similar to the Grüss one and applications for quadrature rules are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 257 - 266
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Cerone, P. and Dragomir, S.S., ‘A refinement of the Grüss inequality and applications’, J. Inequal. Pure Appl. Math. 5 (2002). Article 14 [ONLINE:http://rgmia.vu.edu.au/v5n2.html].Google Scholar
[2]Dragomir, S.S., ‘On the Ostrowski's inequality for Riemann-Stieltjes integral and applications’, Korean J. Comput. and Appl. Math. 7 (2000), 611–627.CrossRefGoogle Scholar
[3]Dragomir, S.S., ‘Some inequalities for Riemann-Stieltjes integral and applications’, in Optimisation and Related Topics, (Rubinov, A., Editor), Appl. Optim. 47 (Kluwer Academic Publishers, Dorchrecht, 2000), pp. 197–235.CrossRefGoogle Scholar
[4]Dragomir, S.S., ‘Some inequalities of midpoint and trapezoid type for the Riemann-Stieltjes integral’, Nonlinear Anal. 47 (2001), 2333–234.CrossRefGoogle Scholar
[5]Dragomir, S.S., ‘On the Ostrowski inequality for Riemann-Stieltjes integral where f is of Hölder type and u is of bounded variation and applications’, J. KSIAM 5 (2001), 35–45.Google Scholar