Some sharp inequalities involving Seiffert and other means and their concise proofs

Details Some sharp inequalities involving Seiffert and other means and their concise proofs Some sharp inequalities involving Seiffert and other means and their concise proofs

2012-01-31

arxiv.org/abs/1201.6480v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

In the paper, by establishing the monotonicity of some functions involving
the sine and cosine functions, the authors provide concise proofs of some known
inequalities and find some new sharp inequalities involving the Seiffert,
contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square
means of two positive real numbers $a$ and $b$ with $a\ne b$.

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