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Element, Mathematical Inequalities and Applications, 4, p. 1007-1017, 2012

DOI: 10.7153/mia-15-86

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

Journal article published in 2012 by Wei-Dong Jiang, Feng Qi ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide a unified and concise proof 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 not equal b.