Abstract and Applied Analysis

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

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

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Abstract

We answer the question: for α ( 0 , 1 ) , what are the greatest value p and the least value q such that the double inequality M p ( a , b ) < P α ( a , b ) G 1 α ( a , b ) < M q ( a , b ) holds for all a , b > 0 with a 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


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