Abstract
In this paper, some Grüss-type results via Pompeiu’s-like inequalities are proved.
References
Acu, A.M.; Sofonea, F.D.: On an inequality of Ostrowski type. J. Sci. Arts 3(16), 281–287 (2011)
Acu, A.M.; Baboş, A.; Sofonea, F.D.: The mean value theorems and inequalities of Ostrowski type. Sci. Stud. Res. Ser. Math. Inform. 21(1), 5–16 (2011)
Cerone, P.; Dragomir, S.S.: New bounds for the Čebyšev functional. Appl. Math. Lett. 18, 603–611 (2005)
Cerone, P.; Dragomir, S.S.: A refinement of the Grüss inequality and applications. Tamkang J. Math. 38(1), 37–49 (2007)
Cerone, P.; Dragomir, S.S.: Some bounds in terms of \({\Delta}\)-seminorms for Ostrowski-Grüss type inequalities. Soochow J. Math. 27(4), 423–434 (2001)
Cerone, P.; Dragomir, S.S.; Roumeliotis, J. Grüss inequality in terms of \({\Delta}\)-seminorms and applications. Integr. Transforms Spec. Funct. 14(3), 205–216 (2003)
Chebyshev, P.L.: Sur les expressions approximatives des intè grals dèfinis par les outres prises entre les même limites. Proc. Math. Soc. Charkov 2, 93–98 (1882)
Cheng, X-L.; Sun, J.: Note on the perturbed trapezoid inequality. J. Ineq. Pure Appl. Math. 3(2), (2002) (art. 29, 7 pp)
Dragomir, S.S.: An inequality of Ostrowski type via Pompeiu’s mean value theorem. J. Inequal. Pure Appl. Math. 6(3), (2005) (article 83, 9 pp)
Grüss, G.: Über das Maximum des absoluten Betrages von \({\frac{1}{b-a}\int_{a}^{b}f(x)g(x)dx-\frac{1}{\left( b-a\right) ^{2}}\int_{a}^{b}f(x)dx\int_{a}^{b}g(x)dx}\). Math. Z. 39, 215–226 (1935)
Li, X.; Mohapatra, R.N.; Rodriguez, R.S.: Grüss-type inequalities. J. Math. Anal. Appl. 267(2), 434–443 (2002)
Lupaş, A.: The best constant in an integral inequality. Mathematica (Cluj, Romania) 15(38)(2), 219–222 (1973)
Mercer, A.M.: An improvement of the Grüss inequality. J. Inequal. Pure Appl. Math. 6(4), (2005) (article 93, 4 pp)
Mitrinović, D.S.; Pečarić, J.E.; Fink, A.M.: Classical and New Inequalities in Analysis. Kluwer Academic Publishers, Dordrecht/Boston/London (1993)
Ostrowski, A.M.: On an integral inequality. Aequat. Math. 4, 358–373 (1970)
Pachpatte, B.G.: On Grüss like integral inequalities via Pompeiu’s mean value theorem. J. Inequal. Pure Appl. Math. 6(3), (2005) (article 82, 5 pp)
Pečarić, J.; Ungar, Š.: On an inequality of Ostrowski type. J. Inequal. Pure Appl. Math. 7(4), (2006) (art. 151, 5 pp)
Pompeiu D.: Sur une proposition analogue au théorème des accroissements finis. Mathematica (Cluj, Romania) 22, 143–146 (1946)
Popa E.C.: An inequality of Ostrowski type via a mean value theorem. Gen. Math. 15(1), 93–100 (2007)
Sahoo, P.K.; Riedel, T.: Mean Value Theorems and Functional Equations. World Scientific, Singapore, New Jersey, London, Hong Kong (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Dragomir, S.S. Some Grüss-type results via Pompeiu’s-like inequalities. Arab. J. Math. 4, 159–170 (2015). https://doi.org/10.1007/s40065-015-0135-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-015-0135-8
Mathematics Subject Classification
- 26D15
- 25D10