WEIGHTED OSTROWSKI AND CEBYSEV TYPE INEQUALITIES WITH APPLICATIONS

Year 2013, Volume: 1 Issue: 2, 1 - 16, 01.12.2013

S. Hussaın M. W.alomarı

Abstract

Weighted Ostrowski and ˇCebyˇsev type inequalities on time scalesfor single and double integrals have been derived which unify the correspondingcontinuous and discrete versions and some applications for quantum calculusare also given

Keywords

Ostrowski and ˇCebyˇsev inequalities, Time scales; Montgomeryidentity

References

• Bohner, M. and Lutz, D. A., Asymptotic behaviour of dynamic equations on time scales J. Differ. Equations Appl., 7(1) (2001) 21-50.
• Boukerrioua, K. and Guezane-Lakoud, A., On Generalization of ˇCebyˇsev type inequalities, J. Inequal. Pure and Appl. Math., 8 (2) 2007.
• Barnet, N. S., Ceron, P., Dragomir, S. S., Pinheiro, M. R. and Sofo, A., Ostrowski type inequalities for functions whose modulus of derivatives are convex and applications, RGMIA Res. Collec., 5 (2) (2002) 219-231.
• Cerone, P. and Dragomir, S.S., Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Math., 37 (2) (2004) 299-308.
• ˇCebyˇsev, P. L., Sur les expressions approximative des integrals par les auters prises entre les mˆemes limites, Proc. Math. Soc. Charkov, 2 (1882), 93-98.
• Dragomir, S.S. and Rassias, Th. M., (Eds.), Ostrowski type inequalities and applications in Numerical integration, Kluwer Academic Publishers, Dordrect, 2002.
• Dragomir, S.S. and Sofo, A., Ostrowski type inequalities for functions whose derivatives are convex, Proceedind of the 4th International Conference on Modelling and Simulation, November 2002. Victoria University, Melbourne Australia, RGMIA Res. Rep. Collec., 5 (2002) Supp., Art. 30.
• Basak Karpuz and Umut Mutlu ¨Ozkan, Generalized ostrowski’s inequality on time scales, J. Inequal. Pure and Appl. Math., 9 (4) 2008.
• Mitrinovi´c, D. S., Peˇcari´c, J. E. and Fink, A. M., Inequalities involving functions and their integrals and derivatives, Mathematics and its applications, Dordrecht, Kluwer Academic Publishers, Vol. 53, 1991.
• Mitrinovi´c, D. S., Peˇcari´c, J. E. and Fink, A. M., Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht, 1993.
• Ostrowski, A., ¨Uber die absolutabweichung einer differentierbaren funktion von ihren inte- gralmittelwert, Comment. Math. Helv., 10 (1938), 226-227.
• Ozkan, U. M., Sarikaya M. Z., and Yildirim, H., Extensions of certain integral inequalities on time scales, Applied Mathematics Letters, 21 (10) (2008), 993–1000.
• Peˇcari´c, J. E., On the ˇCebysev inequality, Bul. Sti. Tehn. Inst. Politehn. Tralan Vuia Timisora (Romania), 25 (39) (1) (1980), 5-9.
• Pachpatte, B. G., On Ostrowski-Gr¨uss- ˇCebyˇsev type inequalities for functions whose modulus of derivatives are convex, JIPAM 6(4) (2005) 1-14.
• Peˇcari´c, J. E., Proschan F. and Tang Y. L., Convex functions, Partial orderings and statistical Applications, Academic Press, New York, 1991.
• Sarikaya, M. Z., A Note on Gr¨uss type inequalities on time scales, Dynamic Systems and Applications, 17 (2008), 663-666.
• Sarikaya, M. Z., On weighted Iyengar type inequalities on time scales, Applied Mathematics Letters, 22 (2009), 1340–1344. [18] Sarikaya, M. Z., Aktan, N., and Yildirim, H., On Cebyˇsev–Gr¨uss type inequalities on time scales, Journal of Mathematical Inequalities, Volume 2, Number 2 (2008), 185–195.
• 1Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan.
• E-mail address: [e-mail] 2
• Department of Mathematics, Faculty of Science, Jerash University, 26150 Jerash, Jordan.
• E-mail address: [e-mail]