Table of Contents
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 829158, 4 pages
http://dx.doi.org/10.1155/2014/829158
Research Article

On Hermite-Hadamard Type Inequalities for Functions Whose Second Derivatives Absolute Values Are -Convex

School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China

Received 5 September 2013; Accepted 6 November 2013; Published 5 February 2014

Academic Editors: Y.-D. Kwon, Y. Wang, X.-S. Yang, and W. Yeih

Copyright © 2014 Feixiang Chen and Xuefei Liu. 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. G. Farid, S. Abramovich, and J. Pečarić, “More about hermite-hadamard inequalities, cauchy's means, and superquadracity,” Journal of Inequalities and Applications, vol. 2010, Article ID 102467, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. M. W. Alomari, M. Darus, and U. S. Kirmaci, “Some inequalities of Hermite-Hadamard type for s-convex functions,” Acta Mathematica Scientia, vol. 31, no. 4, pp. 1643–1652, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. M. Bessenyei and Z. Páles, “Hadamard-type inequalities for generalized convex functions,” Mathematical Inequalities and Applications, vol. 6, no. 3, pp. 379–392, 2003. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. S. S. Dragomir, J. Pecaric, and Persson, “Some inequalities of Hadamard type,” Soochow Journal of Mathematics, no. 21, pp. 335–341, 1995. View at Google Scholar
  5. A. El Farissi, “Simple proof and refinement of Hermite-Hadamard inequality,” Journal of Mathematical Inequalities, vol. 4, no. 3, pp. 365–369, 2010. View at Google Scholar
  6. X. Gao, “A note on the Hermite-Hadamard inequality,” Journal of Mathematical Inequalities, vol. 4, no. 4, pp. 587–591, 2010. View at Google Scholar
  7. H. Kavurmaci, M. Avci, and M. E. Özdemir, “New inequalities of Hermite-Hadamard type for convex functions with applications,” Journal of Inequalities and Applications, vol. 2011, p. 86, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. U. S. Kirmaci, M. Klaričić Bakula, M. E. Özdemir, and J. Pečarić, “Hadamard-type inequalities for s-convex functions,” Applied Mathematics and Computation, vol. 193, no. 1, pp. 26–35, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. C. E. M. Pearce and J. Pečcarić, “Inequalities for differentiable mappings with application to special means and quadrature formula,” Applied Mathematics Letters, vol. 2, no. 13, pp. 51–55, 2000. View at Google Scholar
  10. 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 · View at Scopus
  11. S. S. Dragomir and S. Fitzpatrick, “The Hadamard inequalities for s-convex functions in the second sense,” Demonstration Mathematics, vol. 32, no. 4, pp. 687–696, 1999. View at Google Scholar
  12. A. Barani, S. Barani, and S. S. Dragomir, “Refinements of Hermite-Hadamard inequalities for functions when a power of the absolute value of the second derivative is P-convex,” Journal of Applied Mathematics, vol. 2012, Article ID 615737, 10 pages, 2012. View at Publisher · View at Google Scholar
  13. 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 ID 69, 2011. View at Google Scholar
  14. S. Hussain, M. I. Bhatti, and M. Iqbal, “Hadamard-type inequalities for s-convex functions I,” Punjab University Journal of Mathematics, vol. 41, pp. 51–60, 2009. View at Google Scholar