József Sándor

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

Volume 21, 2015, Number 1, Pages 31—35

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## Details

### Authors and affiliations

József Sándor

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

### Abstract

By using the basic logarithmic inequality ln *x* ≤ *x* − 1 we deduce integral inequalities, which particularly imply the inequalities *G* < *L* < *A* for the geometric, logarithmic, resp. arithmetic means.

### Keywords

- Logaritmic function
- Logarithmic mean
- Means and their inequalities

### AMS Classification

- 26D15
- 26D99

### References

- Carlson, B. C. (1966) Some inequalities for hypergeometric functions, Proc. Amer. Math.Soc.,17, 32–39
- Carlson, B. C. (1972) The logarithmic mean, Amer. Math. Monthly, 79, 615–618.
- Ostle, B., & Terwilliger, H. L. (1957) A comparison of two means, Proc. Montana Acad.Sci., 17, 69–70.
- Sándor, J. (1990) On the identric and logarithmic means, Aeq. Math., 40, 261–270.
- Lorenzen, G. (1994) Why means in two arguments are special, Elem. Math., 49, 32–37.

## Related papers

## Cite this paper

APASándor, J. (2015). A basic logarithmic inequality, and the logarithmic mean. Notes on Number Theory and Discrete Mathematics, 21(1), 31-35.

ChicagoSándor, József. “A Basic Logarithmic Inequality, and the Logarithmic Mean.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 31-35.

MLASándor, József. “A Basic Logarithmic Inequality, and the Logarithmic Mean.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 31-35. Print.