A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means

Wei-Ming Gong, Ying-Qing Song, Miao-Kun Wang and Yu-Ming Chu

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: For fixed s ≥ 1 and any t1, t2 ∈ (0,1/2) we prove that the double inequality Gs(t1a + (1 − t1)b, t1b + (1 − t1)a)A1−s(a, b) 0 with a ≠ b if and only if t1≤(1-12-(/π) 2/s)/2 and t2≥(112-/3s)/. Here, P(a, b), A(a, b) and G(a, b) denote the Seiffert, arithmetic, and geometric means of two positive numbers a and b, respectively.

Date: 2012
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https://doi.org/10.1155/2012/684834

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:684834

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