An Elementary Proof of the Mean Inequalities

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DOI: 10.4236/apm.2013.33047    3,949 Downloads   6,932 Views   Citations

In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

I. Izmirli, "An Elementary Proof of the Mean Inequalities," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 331-334. doi: 10.4236/apm.2013.33047.

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