On upper Hermite–Hadamard inequalities for geometric-convex and log-convex functions

József Sándor
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 5, Pages 25–30
Full paper (PDF, 142 Kb)
Corrigendum (PDF, 101 Kb)

Details

Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University,
Str. Kogălniceanu nr. 1, 400084 Cluj-Napoca, Romania

Abstract

We offer connections between upper Hermite–Hadarmard type inequalities for geometric convex and logarithmically convex functions.

Keywords

• Integral inequalities
• Geometric convex functions
• log-convex functions

AMS Classification

• 26D15
• 26D99
• 26A51

References

1. Gill, P. M., C. E. M. Pearce, J. Pečarić, Hadamard’s inequality for r-convex functions,J. Math. Anal. Appl., Vol. 215, 1997, No. 2, 461–470
2. Iscan, I. Some new Hermite–Hadamard type inequalities for geometrically convex functions,Math. and Stat., Vol. 1, 2013, No. 2, 86–91
3. Neuman, E., J. Sándor, Inequalities involving Stolarsky and Gini means, Math. Pannonica, Vol. 14, 2003, No. 1, 29–44
4. Niculescu, C. P., L.-E. Persson, Convex Functions and Their Applications, CMS Books in Math., Springer, 2005.
5. Sándor, J. On certain weighted means, Octogon Math. Mag., Vol. 20, 2012, No. 1, 149–157
6. Xi, B.-Y., F. Qi, Integral inequalities and Simpson type for logarithmically convex functions, Adv. Stud. Contemp. Math. , Vol. 23, 2013, No. 4, 559–566.
7. Roberts, A. W., D. E. Varberg, Convex Functions , Academic Press, New York, 1973