József Sándor and Edith Egri

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 21, 2015, Number 4, Pages 40–47

**Full paper (PDF, 168 Kb)**

## Details

### Authors and affiliations

József Sándor

*Babes–Bolyai University, Department of Mathematics,
Cluj-Napoca, Romania
*

Edith Egri

*Babes–Bolyai University, Department of Mathematics,
Cluj-Napoca, Romania
*

### Abstract

We consider certain properties of functions *f* : *J* → *I* (*I*, *J* intervals) such that

*f*(*M*(*x*, *y*)) ≤ *N*(*f*(*x*), *f*(*y*)), where *M* and *N* are general means. Some results are extensions of the case *M = N = L*, where *L* is the logarithmic mean.

### Keywords

- Mean
- Logarithmic mean
- Identric mean
- Integral mean
- Convex or concave functions with respect to a mean
- Subadditive functions
- Continuity

### AMS Classification

- 26A51
- 26D99
- 39B72

### References

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## Cite this paper

Sándor, J., & Egri, E. (2015). On (*M*, *N*)-convex functions. *Notes on Number Theory and Discrete Mathematics*, 21(4), 40-47.