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Journal of Function Spaces and Applications
Volume 2012, Article ID 980438, 14 pages
http://dx.doi.org/10.1155/2012/980438
Research Article

Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

Bo-Yan Xi1 and Feng Qi2,3

1College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City 028043, China
2School of Mathematics and Informatics, Henan Polytechnic University, Henan Province, Jiaozuo City 454010, China
3Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City 300387, China

Received 21 February 2012; Accepted 21 May 2012

Academic Editor: Lars Diening

Copyright © 2012 Bo-Yan Xi and Feng Qi. 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.

Citations to this Article [27 citations]

The following is the list of published articles that have cited the current article.

  • Shu-Ping Bai, Shu-Hong Wang, and Feng Qi, “Some Hermite-Hadamard type inequalities for n-time differentiable (alpha, m)-convex functions,” Journal Of Inequalities And Applications, 2012. View at Publisher · View at Google Scholar
  • Bo-Yan Xi, Shu-Hong Wang, and Feng Qi, “Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex,” Analysis (Germany), vol. 32, no. 3, pp. 247–262, 2012. View at Publisher · View at Google Scholar
  • Ling Chun, and Feng Qi, “Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex,” Applied Mathematics, vol. 03, no. 11, pp. 1680–1685, 2012. View at Publisher · View at Google Scholar
  • Boyan Xi, Shuhong Wang, and Feng Qi, “Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>P</i>-Convex,” Applied Mathematics, vol. 03, no. 12, pp. 1898–1902, 2012. View at Publisher · View at Google Scholar
  • Ye Shuang, Hong-Pin Yin, and Feng 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
  • Mevlüt Tunç, “Some Hadamard-Like Inequalities via Convex and s-Convex Functions and their Applications for Special Means,” Mediterranean Journal of Mathematics, 2013. View at Publisher · View at Google Scholar
  • Jaekeun Park, “Some generalized inequalities of hermite-hadamard type for (α,m)-geometric-arithmetically convex functions,” Applied Mathematical Sciences, vol. 7, no. 93-96, pp. 4743–4759, 2013. View at Publisher · View at Google Scholar
  • Jaekeun Park, “Some hermite-hadamard-like type inequalities for logarithmically convex functions,” International Journal of Mathematical Analysis, vol. 7, no. 45-48, pp. 2217–2233, 2013. View at Publisher · View at Google Scholar
  • Bo-Yan Xi, “Some integral inequalities of Simpson type for GA-epsilon-convex functions,” Georgian Mathematical Journal, vol. 20, no. 4, pp. 775–788, 2013. View at Publisher · View at Google Scholar
  • Rui-Fang Bai, Bo-Yan Xi, and Feng Qi, “Hermite-Hadamard type inequalities for the m- and (alpha, m)-logarithmically convex functions,” Filomat, vol. 27, no. 1, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Wen-Hui Li, and Feng Qi, “Some Hermite-Hadamard type inequalities for functions whose n-th derivatives are (alpha, m)-convex,” Filomat, vol. 27, no. 8, pp. 1575–1582, 2013. View at Publisher · View at Google Scholar
  • Feng Qi, and Bo-Yan Xi, “Some Hermite–Hadamard type inequalities for geometrically quasi-convex functions,” Proceedings - Mathematical Sciences, 2014. View at Publisher · View at Google Scholar
  • Muhammad Amer Latif, and Muhammad Shoaib, “Hermite–Hadamard type integral inequalities for differentiable m-preinvex and (α,m)-preinvex functions,” Journal of the Egyptian Mathematical Society, 2014. View at Publisher · View at Google Scholar
  • Bo-Yan Xi, Feng Qi, and Jü Hua, “Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle,” Journal of Applied Analysis, vol. 20, no. 1, pp. 29–39, 2014. View at Publisher · View at Google Scholar
  • Jaekeun Park, “Hermite-Hadamard type inequalities for functions whose third derivatives are convex and s-convex,” Applied Mathematical Sciences, vol. 8, no. 1-4, pp. 13–31, 2014. View at Publisher · View at Google Scholar
  • Jaekeun Park, “Generalization of Hermite-Hadamard type inequality for functions whose derivatives in absolute value are convex and (α,m)-convex,” Applied Mathematical Sciences, vol. 8, no. 45-48, pp. 2307–2325, 2014. View at Publisher · View at Google Scholar
  • Imdat Işcan, “Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions,” Journal of Mathematics, vol. 2014, 2014. View at Publisher · View at Google Scholar
  • Banyat Sroysang, “Generalizations on Some Hermite-Hadamard Type Inequalities for Differentiable Convex Functions with Applications to Weighted Means,” The Scientific World Journal, vol. 2014, pp. 1–13, 2014. View at Publisher · View at Google Scholar
  • Shu-Hong Wang, and Feng Qi, “Hermite-Hadamard type inequalities for n-times differentiable and preinvex functions,” Journal of Inequalities and Applications, vol. 2014, no. 1, pp. 49, 2014. View at Publisher · View at Google Scholar
  • Yan Wang, Miao-Miao Zheng, and Feng Qi, “Integral inequalities of Hermite-Hadamard type for functions whose derivatives are α-preinvex,” Journal of Inequalities and Applications, vol. 2014, no. 1, pp. 97, 2014. View at Publisher · View at Google Scholar
  • Muhammad Amer Latif, “Some new hermite-hadamard type inequalities for functions whose higher order partial derivatives are co-ordinated s-convex,” Kragujevac Journal of Mathematics, vol. 38, no. 1, pp. 125–146, 2014. View at Publisher · View at Google Scholar
  • Jü Hua, Bo-Yan Xi, and Feng 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 Publisher · View at Google Scholar
  • F. Qi, T. -Yu Zhang, and B. -Ya. Xi, “Hermite-Hadamard-Type Integral Inequalities for Functions Whose First Derivatives are Convex,” Ukrainian Mathematical Journal, vol. 67, no. 4, pp. 625–640, 2015. View at Publisher · View at Google Scholar
  • Mevlüt Tunç, and Ümmügülsüm Şanal, “Some perturbed trapezoid inequalities for convex, s-convex and tgs-convex functions and applications,” Tbilisi Mathematical Journal, vol. 8, no. 2, 2015. View at Publisher · View at Google Scholar
  • Sever S. Dragomir, “Integral inequalities for lipschitzian mappings between two banach spaces and applications,” Kodai Mathematical Journal, vol. 39, no. 1, pp. 227–251, 2016. View at Publisher · View at Google Scholar
  • Ying Wu, and Feng Qi, “On some Hermite-Hadamard type inequalities for (s, QC)-convex functions,” Springerplus, vol. 5, 2016. View at Publisher · View at Google Scholar
  • Çetin Yildiz, “New inequalities of the hermite-hadamard type for n-time differentiable functions which are quasiconvex,” Journal of Mathematical Inequalities, vol. 10, no. 3, pp. 703–711, 2016. View at Publisher · View at Google Scholar