## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 108920, 12 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620768

Digital Object Identifier
doi:10.1155/2010/108920

Mathematical Reviews number (MathSciNet)
MR2720028

Zentralblatt MATH identifier
1197.26054

#### Citation

Chu, Yu-Ming; Qiu, Ye-Fang; Wang, Miao-Kun. Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means. Abstr. Appl. Anal. 2010 (2010), Article ID 108920, 12 pages. doi:10.1155/2010/108920. https://projecteuclid.org/euclid.aaa/1288620768