Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-05T14:35:07.075Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME RESULTS ON COMPARING TWO INTEGRAL MEANS FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS

Part of: Inequalities

Published online by Cambridge University Press:  10 April 2014

DAH-YAN HWANG  and
SILVESTRU SEVER DRAGOMIR
DAH-YAN HWANG*
Affiliation:
Department of Information and Management, Taipei Chengshih University of Science and Technology, No. 2, Xueyuan Rd., Beitou, 112 Taipei, Taiwan email dyhuang@tpcu.edu.tw
SILVESTRU SEVER DRAGOMIR
Affiliation:
Mathematics, School of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia email sever.dragomir@vu.edu.au School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
*
✉dyhuang@tpcu.edu.tw
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some better estimates for the difference between the integral mean of a function and its mean over a subinterval are established. Various applications for special means and probability density functions are also given.

Keywords

Grüss inequalityOstrowski’s inequalityintegral meansspecial meanprobability density function

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals 26D10: Inequalities involving derivatives and differential and integral operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 264 - 274
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Anastassiou, G. A., ‘High order Ostrowski type inequalities’, Appl. Math. Lett. 20 (2007), 616–621.CrossRefGoogle Scholar
Barnett, N. S., Bus, C., Cerone, E. P. and Dragomir, S. S., ‘Ostrowskis inequality for vector-valued functions and applications’, Comput. Math. Appl. 44 (2002), 559–572.Google Scholar
Barnett, N. S., Cerone, P., Dragomir, S. S. and Fink, A. M., ‘Comparing two integral means for absolutely continuous mappings whose derivatives are in L ∞[a, b] and applications’, Comput. Math. Appl. 44 (2002), 241–251.Google Scholar
Cerone, P., Cheung, W. S. and Dragomir, S. S., ‘On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation’, Comput. Math. Appl. 54 (2007), 183–191.Google Scholar
Cerone, P. and Dragomir, S. S., ‘A refinenement of the Grüss inequality and applications’, Tamkang J. Math. 38 (2007), 37–49; Preprint, RGMIA Res. Rep. Coll., 5, 2002, 2, Article 14.Google Scholar
Cheng, X. L., ‘Improvement of some Ostrowski–Grüss type inequalities’, Comput. Math. Appl. 42 (2001), 109–114.CrossRefGoogle Scholar
Cheng, X. L. and Sun, J., ‘A note on the perturbed trapezoid inequality’, J. Ineq. Pure. and Appl. Math. 3 (2002), Article 29.Google Scholar
Dragomir, S. S., ‘Bounds for some perturbed Chebyshev functionals’, J. Inequal. Pure Appl. Math. 9 (2008), Art. 64.Google Scholar
Dragomir, S. S. and Sofo, A., ‘An inequality for monotonic functions generalizing Ostrowski and related results’, Comput. Math. Appl. 51 (2006), 497–506.Google Scholar
Dragomir, S. S. and Wang, S., ‘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’, Comput. Math. Appl. 33 (1997), 15–20.Google Scholar
Dragomir, S. S. and Wang, S., ‘Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rules’, Appl. Math. Lett. 11 (1998), 105–109.Google Scholar
Fedotov, I. and Dragomir, S. S., ‘An inequality of Ostrowski type and its applications for Simpson’s rule and special means’, Math. Inequal. Appl. 2 (1999), 491–499.Google Scholar
Liu, W. J., ‘Several error inequalities for a quadrature formula with a parameter and applications’, Comput. Math. Appl. 56 (2008), 1766–1772.Google Scholar
Liu, Z., ‘Some Ostrowski–Grüss type inequalities and applications’, Comput. Math. Appl. 53 (2007), 73–79.Google Scholar
Liu, Z., ‘Some Ostrowski type inequalities’, Math. Comput. Modelling 48 (2008), 949–960.Google Scholar
Liu, W. J., Xue, Q. L. and Wang, S. F., ‘Several new perturbed Ostrowski-like type inequalities’, J. Inequal. Pure Appl. Math. 8 (2007), 6 Article 110.Google Scholar
Masjed-Jamei, M. and Dragomir, S. S., ‘A new generalization of the Ostrowski inequality and applications’, Filomat 25 (2011), 115–123.Google Scholar
Mitrinović, D. S., Pečarić, J E and Fink, A. M., Classical and New Inequalities in Analysis (Kluwer Academic Publishers, Dordrecht, 1993).Google Scholar
Ostrowski, A., ‘Über die Absolutabweichung einer differentierbaren Funktion von ihren Integralmittelwert’, Comment. Math. Helv. 10 (1938), 226–227.Google Scholar
Pachpatte, B. G., ‘On an inequality of Ostrowski type in three independent variables’, J. Math. Anal. Appl. 249 (2000), 583–591.Google Scholar
Tseng, K. L., Hwang, S. R. and Dragomir, S. S., ‘Generalizations of weighted Ostrowski type inequalities for mappings of bounded variation and their applications’, Comput. Math. Appl. 55 (2008), 1785–1793.Google Scholar
Tseng, K. L., Hwang, S. R., Yang, G. S. and Chou, Y. M., ‘Improvements of the Ostrowski integral inequality for mappings of bounded variation I’, Appl. Math. Comput. 217 (2010), 2348–2355.Google Scholar
Ujević, N., ‘A generalization of Ostrowski’s inequality and applications in numerical integration’, Appl. Math. Lett. 17 (2004), 133–137.Google Scholar
Xue, Q., Zhu, J. and Liu, W., ‘A new generalization of Ostrowski-type inequality involving functions of two independent variables’, Comput. Math. Appl. 60 (2010), 2219–2224.CrossRefGoogle Scholar