József Sándor

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 4, Pages 20—24

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## Details

### Authors and affiliations

József Sándor

*Babeș-Bolyai University
Cluj-Napoca, Romania
*

### Abstract

We show how a logarithmic inequality from the book [1] is connected to means, and we offer new proofs, as well as refinements. We show that Karamata’s [2] and Leach–Sholander’s [3] inequality are in fact equivalent.

### Keywords

- Logarithmic function
- Logarithmic mean
- Leach–Sholander inequality

### AMS Classification

- 26D15
- 26D99

### References

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- Sándor, J. (2015) A note on log–convexity of power means, Ann. Math. Inf., 45, 107–110.
- Sándor, J. (2016) A note on the logarithmic mean, Amer. Math. Monthly, 123(1), 112.
- Sándor, J. (2016) Applications of the Cauch–Bouniakowsky inequality in the theory of means, Adv. Stud. Contemp. Math., 26(2), 237–254.
- Sándor, J. (2016) Series expansions related to the logarithmic mean, Notes Number Th. Discr. Math., 22(2), 54–57.

## Related papers

## Cite this paper

APASándor, J. (2016). On certain logarithmic inequalities. Notes on Number Theory and Discrete Mathematics, 22(4), 20-24.

ChicagoSándor, József. “On Certain Logarithmic Inequalities.” Notes on Number Theory and Discrete Mathematics 22, no. 4 (2016): 20-24.

MLASándor, József. “On Certain Logarithmic Inequalities.” Notes on Number Theory and Discrete Mathematics 22.4 (2016): 20-24. Print.