Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 809689, 12 pages
Research Article

Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable ( 𝛼 , 𝑚 )-Convex Mappings

Department of Mathematics, Hanseo University, Chungnam-do, Seosan-si 356-706, Republic of Korea

Received 13 July 2011; Revised 13 November 2011; Accepted 28 November 2011

Academic Editor: Jewgeni Dshalalow

Copyright © 2012 Jaekeun Park. 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. M. Klaričić Bakula, M. E. Özdemir, and J. Pečarić, “Hadamard type inequalities for m and (α,m)-convex functions,” Journal of Inequalities in Pure and Applied Mathematics, vol. 9, no. 4, article 96, p. 12, 2008. View at Google Scholar
  2. M. E. Özdemir, E. Set, and M. Z. Sarikaya, “Some new Hadamard’s type inequalities for co-ordinated m-convex and (α,m)-convex functions,”
  3. M. E. Özdemir, M. Avci, and H. Kavurmaci, “Hermite-Hadamard-type inequalities via α,m-convexity,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2614–2620, 2011. View at Publisher · View at Google Scholar
  4. E. Set, M. E. Özdemir, and M. Z. Sarikaya, “Inequalities of Hermite-Hadamard’s type for functions whose derivatives absolute values are m-convex,” in Proceedings of the AIP Conference, vol. 1309, pp. 861–873, 2010,
  5. M. Alomari and M. Darus, “On some inequalities of Simpson-type via quasi-convex functions and applications,” Transylvanian Journal of Mathematics and Mechanics, vol. 2, no. 1, pp. 15–24, 2010. View at Google Scholar
  6. J. Park, “Generalizations of simpson-like type inequalities for differentiable m-convex and (α,m) -convex mappings,” Far East Journal of Mathematical Sciences, vol. 55, no. 1, pp. 97–109, 2011. View at Google Scholar
  7. M. Z. Sarikaya, E. Set, and M. E. Özdemir, “On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex,” RGMIA Research Report Collection, vol. 13, no. 1, article 1, 2010. View at Google Scholar
  8. G. Toader, “The hierarchy of convexity and some classic inequalities,” Journal of Mathematical Inequalities, vol. 3, no. 3, pp. 305–313, 2009. View at Google Scholar · View at Zentralblatt MATH
  9. S. S. Dragomir, R. P. Agarwal, and P. Cerone, “On Simpson's inequality and applications,” Journal of Inequalities and Applications, vol. 5, no. 6, pp. 533–579, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH