Skip to content


  • Research Article
  • 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:


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


  • Special Domain
  • Homogeneous Function


Authors’ Affiliations

Department of Mathematics, Akdeniz University, Antalya, 07058, Turkey


  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