Table of Contents
International Journal of Analysis
Volume 2014, Article ID 125439, 6 pages
http://dx.doi.org/10.1155/2014/125439
Research Article

Hermite-Hadamard and Simpson Type Inequalities for Differentiable P-GA-Functions

Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun, Turkey

Received 21 February 2014; Accepted 14 May 2014; Published 22 May 2014

Academic Editor: Seenith Sivasundaram

Copyright © 2014 İmdat İşcan. 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. 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 MathSciNet
  2. C. P. Niculescu, “Convexity according to the geometric mean,” Mathematical Inequalities & Applications, vol. 3, no. 2, pp. 155–167, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  3. C. P. Niculescu, “Convexity according to means,” Mathematical Inequalities & Applications, vol. 6, no. 4, pp. 571–579, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Barani and S. Barani, “Hermite-Hadamard type inequalities for functions when a power of the absolute value of the first derivative is P-convex,” Bulletin of the Australian Mathematical Society, vol. 86, no. 1, pp. 126–134, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. Hua, B.-Y. Xi, and F. Qi, “Hermite-Hadamard type inequalities for geometric-arithmetically s-convex functions,” Communications of the Korean Mathematical Society, vol. 29, no. 1, pp. 51–63, 2014. View at Google Scholar
  6. İ. İşcan, “Some new general integral inequalities for h-convex and h-concave functions,” Advances in Pure and Applied Mathematics, vol. 5, no. 1, pp. 21–29, 2014. View at Publisher · View at Google Scholar
  7. İ. İşcan, “Hermite-Hadamard type inequalities for GA-s-convex functions,” Le Matematiche. In press.
  8. M. E. Özdemir and Ç. Yıldız, “New inequalities for Hermite-Hadamard and Simpson type with applications,” Tamkang Journal of Mathematics, vol. 44, no. 2, pp. 209–216, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Y. Shuang, H.-P. Yin, and F. Qi, “Hermite-Hadamard type integral inequalities for geometric-arithmetically s-convex functions,” Analysis, vol. 33, no. 2, pp. 197–208, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  10. X.-M. Zhang, Y.-M. Chu, and X.-H. Zhang, “The Hermite-Hadamard type inequality of GA-convex functions and its applications,” Journal of Inequalities and Applications, vol. 2010, Article ID 507560, 11 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. T.-Y. Zhang, A.-P. Ji, and F. Qi, “Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means,” Le Matematiche, vol. 68, no. 1, pp. 229–239, 2013. View at Publisher · View at Google Scholar · View at MathSciNet