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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 428983, 10 pages
On New Inequalities via Riemann-Liouville Fractional Integration
1Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
2Department of Mathematics, Faculty of Science and Arts, Afyon Kocatepe University, Afyon, Turkey
Received 9 August 2012; Accepted 6 October 2012
Academic Editor: Ciprian A. Tudor
Copyright © 2012 Mehmet Zeki Sarikaya and Hasan Ogunmez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. M. Ostrowski, “Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert,” Commentarii Mathematici Helvetici, vol. 10, pp. 226–227, 1938.
- D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, vol. 53, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
- P. Cerone and S. S. Dragomir, “Trapezoidal-type rules from an inequalities point of view,” in Handbook of Analytic-Computational Methods in Applied Mathematics, pp. 65–134, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2000.
- J. Duoandikoetxea, “A unified approach to several inequalities involving functions and derivatives,” Czechoslovak Mathematical Journal, vol. 51, no. 126, pp. 363–376, 2001.
- S. S. Dragomir and N. S. Barnett, “An Ostrowski type inequality for mappings whose second derivatives are bounded and applications,” RGMIA Research Report Collection, vol. 1, pp. 67–76, 1999.
- S. S. Dragomir, “An Ostrowski type inequality for convex functions,” Univerzitet u Beogradu. Publikacije Elektrotehničkog Fakulteta. Serija Matematika, vol. 16, pp. 12–25, 2005.
- Z. Liu, “Some companions of an Ostrowski type inequality and applications,” Journal of Inequalities in Pure and Applied Mathematics, vol. 10, no. 2, article 52, 12 pages, 2009.
- M. Z. Sarikaya, “On the Ostrowski type integral inequality,” Acta Mathematica Universitatis Comenianae, vol. 79, no. 1, pp. 129–134, 2010.
- M. Z. Sarikaya, “On the Ostrowski type integral inequality for double integrals,” Demonstratio Mathematica, vol. 45, no. 3, pp. 533–540, 2012.
- M. Z. Sarikaya and H. Ogunmez, “On the weighted Ostrowski-type integral inequality for double integrals,” Arabian Journal for Science and Engineering, vol. 36, no. 6, pp. 1153–1160, 2011.
- R. Gorenflo and F. Mainardi, Fractionalcalculus: Integral and Differentiable Equations of Fractional Order, Springer, Wien, Austria, 1997.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, NY, USA, 1993.
- G. Anastassiou, M. R. Hooshmandasl, A. Ghasemi, and F. Moftakharzadeh, “Montgomery identities for fractional integrals and related fractional inequalities,” Journal of Inequalities in Pure and Applied Mathematics, vol. 10, no. 4, article 97, 6 pages, 2009.
- S. Belarbi and Z. Dahmani, “On some new fractional integral inequalities,” Journal of Inequalities in Pure and Applied Mathematics, vol. 10, no. 3, article 86, 5 pages, 2009.
- Z. Dahmani, L. Tabharit, and S. Taf, “Some fractional integral inequalities,” Nonlinear Science Letters, vol. 2, no. 1, pp. 155–160, 2010.
- Z. Dahmani, L. Tabharit, and S. Taf, “New inequalities via Riemann-Liouville fractional integration,” Journal of Advanced Research in Scientific Computing, vol. 2, no. 1, pp. 40–45, 2010.