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Journal of Function Spaces and Applications
Volume 2012, Article ID 980438, 14 pages
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.


The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.