Journal of Applied Mathematics

An Optimal Double Inequality between Seiffert and Geometric Means

Yu-Ming Chu, Miao-Kun Wang, and Zi-Kui Wang

Full-text: Open access

Abstract

For α , β ( 0,1 / 2 ) we prove that the double inequality G ( α a + ( 1 - α ) b , α b + ( 1 - α ) a ) < P ( a , b ) < G ( β a + ( 1 - β ) b , β b + ( 1 - β ) a ) holds for all a , b > 0 with a b if and only if α ( 1 - 1 - 4 / π 2 ) / 2 and β ( 3 - 3 ) / 6 . Here, G ( a , b ) and P ( a , b ) denote the geometric and Seiffert means of two positive numbers a and b, respectively.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 261237, 6 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818673

Digital Object Identifier
doi:10.1155/2011/261237

Mathematical Reviews number (MathSciNet)
MR2854959

Zentralblatt MATH identifier
1235.26011

Citation

Chu, Yu-Ming; Wang, Miao-Kun; Wang, Zi-Kui. An Optimal Double Inequality between Seiffert and Geometric Means. J. Appl. Math. 2011 (2011), Article ID 261237, 6 pages. doi:10.1155/2011/261237. https://projecteuclid.org/euclid.jam/1331818673


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