Abstract and Applied Analysis

Sharp Power Mean Bounds for Sándor Mean

Yu-Ming Chu, Zhen-Hang Yang, and Li-Min Wu

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Abstract

We prove that the double inequality Mp(a,b)<X(a,b)<Mq(a,b) holds for all a,b>0 with ab if and only if p1/3 and qlog 2/(1+log 2)=0.4093…, where X(a,b) and Mr(a,b) are the Sándor and rth power means of a and b, respectively.

Article information

Source
Abstr. Appl. Anal., Volume 2015 (2015), Article ID 172867, 5 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1429103741

Digital Object Identifier
doi:10.1155/2015/172867

Mathematical Reviews number (MathSciNet)
MR3303262

Zentralblatt MATH identifier
1372.26032

Citation

Chu, Yu-Ming; Yang, Zhen-Hang; Wu, Li-Min. Sharp Power Mean Bounds for Sándor Mean. Abstr. Appl. Anal. 2015 (2015), Article ID 172867, 5 pages. doi:10.1155/2015/172867. https://projecteuclid.org/euclid.aaa/1429103741


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