Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means

Yu-Ming Chu; Ye-Fang Qiu; Miao-Kun Wang

doi:10.1155/2010/108920

2010 Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means

Yu-Ming Chu, Ye-Fang Qiu, Miao-Kun Wang

Abstr. Appl. Anal. 2010: 1-12 (2010). DOI: 10.1155/2010/108920

Abstract

We answer the question: for $\alpha \in (0,1)$ , what are the greatest value $p$ and the least value $q$ such that the double inequality ${M}_{p}(a,b)\lt {P}^{\alpha }(a,b){G}^{1-\alpha }(a,b)\lt {M}_{q}(a,b)$ holds for all $a,b>0$ with $a{\,\neq\,}b$ . Here, ${M}_{p}(a,b)$ , $P(a,b)$ , and $G(a,b)$ denote the power of order $p$ , Seiffert, and geometric means of two positive numbers $a$ and $b$ , respectively.

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Yu-Ming Chu, Ye-Fang Qiu, and Miao-Kun Wang "Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means," Abstract and Applied Analysis 2010(none), 1-12, (2010). https://doi.org/10.1155/2010/108920

Published: 2010

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