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Journal of Applied Mathematics
Volume 2012, Article ID 615737, 10 pages
http://dx.doi.org/10.1155/2012/615737
Research Article

Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative Is P-Convex

1Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran
2Department of Civil Engineering, Shahid Chamran University, P.O. Box 135, Ahvaz, Iran
3School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne, MC 8001, Australia
4School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

Received 10 March 2012; Accepted 10 May 2012

Academic Editor: Renat Zhdanov

Copyright © 2012 A. Barani et al. 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.

Linked References

  1. C. E. M. Pearce and J. Pečarić, “Inequalities for differentiable mappings with application to special means and quadrature formula,” Applied Mathematics Letters, vol. 13, no. 2, pp. 51–55, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. M. Alomari, M. Darus, and S. S. Dragomir, “New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex,” Tamkang Journal of Mathematics, vol. 41, no. 4, pp. 353–359, 2010. View at Google Scholar · View at Zentralblatt MATH
  3. A. O. Akdemir and M. E. Ozdemir, “Some Hadamard-type inequalities for coordinated P-convex functions and Godunova-Levin functions,” in Proceedings of the AIP Conference Proceedings, vol. 1309, pp. 7–15, 2010.
  4. A. Barani, A. G. Ghazanfari, and S. S. Dragomir, “Hermite-Hadamard inequality through prequasiinvex functions,” RGMIA Research Report Collection, vol. 14, article 48, 2011. View at Google Scholar
  5. A. Barani, S. Barani, and S. S. Dragomir, “Refinements of Hermite-Hadamard type inequality for functions whose second derivatives absolute values are quasiconvex,” RGMIA Research Report Collection, vol. 14, article 69, 2011. View at Google Scholar
  6. A. Barani and S. Barani, “Hermite-Hadamard inequality for functions whose derivatives absolute values are P-convex,” Bulletin of the Australian Mathematical Society. In press. View at Publisher · View at Google Scholar
  7. S. S. Dragomir and C. E. M. Pearce, “Selected Topics on Hermite-Hadamard Inequalities and Applications,” RGMIA Monographs, Victoria University, 2000, http://ajmaa.org/RGMIA/monographs.php/.
  8. S. S. Dragomir, “Two mappings in connection to Hadamard's inequalities,” Journal of Mathematical Analysis and Applications, vol. 167, no. 1, pp. 49–56, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. S. Dragomir, “On Hadamard’s inequalities for convex functions,” Mathematica Balkanica, vol. 6, pp. 215–222, 1992. View at Google Scholar
  10. S. S. Dragomir, J. E. Pečarić, and J. Sándor, “A note on the Jensen-Hadamard inequality,” L'Analyse Numérique et la Théorie de l'Approximation, vol. 19, no. 1, pp. 29–34, 1990. View at Google Scholar · View at Zentralblatt MATH
  11. S. S. Dragomir, J. Pečarić, and L. E. Persson, “Some inequalities of Hadamard type,” Soochow Journal of Mathematics, vol. 21, no. 3, pp. 335–341, 1995. View at Google Scholar · View at Zentralblatt MATH
  12. S. S. Dragomir and C. E. M. Pearce, “Quasi-convex functions and Hadamard's inequality,” Bulletin of the Australian Mathematical Society, vol. 57, no. 3, pp. 377–385, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. S. Dragomir and R. P. Agarwal, “Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula,” Applied Mathematics Letters. An International Journal of Rapid Publication, vol. 11, no. 5, pp. 91–95, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. D. A. Ion, “Some estimates on the Hermite-Hadamard inequality through quasi-convex functions,” Analele Universit\u a\c tii din Craiova. Seria Matematic\u a-Informatic\u a. Annals of the University of Craiova. Mathematics and Computer Science Series, vol. 34, pp. 83–88, 2007. View at Google Scholar · View at Zentralblatt MATH
  15. M. E. Ozdemir and C. Yildiz, “New inequalities for Hermite-Hadamard and simpson type and applications,” submitted, http://arxiv.org/abs/1103.1965.
  16. K. L. Tseng, G. S. Yang, and S. S. Dragomir, “On quasiconvex functions and Hadamard’s inequality,” RGMIA Research Report Collection, vol. 14, article 1, 2003. View at Google Scholar