Open Access

Hermite-Hadamard-Type Inequalities for Increasing Positively Homogeneous Functions

Journal of Inequalities and Applications20072007:021430

Received: 20 October 2006

Accepted: 6 June 2007

Published: 26 June 2007


We study Hermite-Hadamard-type inequalities for increasing positively homogeneous functions. Some examples of such inequalities for functions defined on special domains are given.


Authors’ Affiliations

Department of Mathematics, Akdeniz University


  1. Dragomir SS, Pearce CEM: Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs. Victoria University, Melbourne City, Australia; 2000. Scholar
  2. Dragomir SS, Pearce CEM: Quasi-convex functions and Hadamard's inequality. Bulletin of the Australian Mathematical Society 1998,57(3):377–385. 10.1017/S0004972700031786MathSciNetView ArticleMATHGoogle Scholar
  3. Pearce CEM, Rubinov AM: -functions, quasi-convex functions, and Hadamard-type inequalities. Journal of Mathematical Analysis and Applications 1999,240(1):92–104. 10.1006/jmaa.1999.6593MathSciNetView ArticleMATHGoogle Scholar
  4. Rubinov AM, Dutta J: Hadamard type inequality for quasiconvex functions in higher dimensions. preprint, RGMIA Res. Rep. Coll., 4(1) 2001, Scholar
  5. Dragomir SS, Pečarić J, Persson LE: Some inequalities of Hadamard type. Soochow Journal of Mathematics 1995,21(3):335–341.MathSciNetMATHGoogle Scholar
  6. Gill PM, Pearce CEM, Pečarić J: Hadamard's inequality for-convex functions. Journal of Mathematical Analysis and Applications 1997,215(2):461–470. 10.1006/jmaa.1997.5645MathSciNetView ArticleMATHGoogle Scholar
  7. Dragomir SS, Dutta J, Rubinov AM: Hermite-Hadamard-type inequalities for increasing convex-along-rays functions. Analysis 2004,24(2):171–181. Scholar
  8. Sharikov EV: Hermite-Hadamard type inequalities for increasing radiant functions. Journal of Inequalities in Pure and Applied Mathematics 2003,4(2):1–13. article no. 47 article no. 47MathSciNetGoogle Scholar
  9. Rubinov A: Abstract Convexity and Global Optimization, Nonconvex Optimization and Its Applications. Volume 44. Kluwer Academic Publishers, Dordrecht, The Netherlands; 2000:xviii+490.View ArticleGoogle Scholar


© G. R. Adilov and S. Kemali 2007

This article is published under license to BioMed Central Ltd. 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.