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2013 Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means
Tie-Hong Zhao, Yu-Ming Chu, Yun-Liang Jiang, Yong-Min Li
Abstr. Appl. Anal. 2013: 1-12 (2013). DOI: 10.1155/2013/348326

Abstract

We prove that the double inequalities I α 1 ( a , b ) Q 1 - α 1 ( a , b ) < M ( a , b ) < I β 1 ( a , b ) Q 1 - β 1 ( a , b ) , I α 2 ( a , b ) C 1 - α 2 ( a , b ) < M ( a , b ) < I β 2 ( a , b ) C 1 - β 2 ( a , b ) hold for all a , b > 0 with a b if and only if α 1 1 / 2 , β 1 log [ 2 log ( 1 + 2 ) ] / ( 1 - log 2 ) , α 2 5 / 7 , and β 2 log [ 2 log ( 1 + 2 ) ] , where I ( a , b ) , M ( a , b ) , Q ( a , b ) , and C ( a , b ) are the identric, Neuman-Sándor, quadratic, and contraharmonic means of a and b , respectively.

Citation

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Tie-Hong Zhao. Yu-Ming Chu. Yun-Liang Jiang. Yong-Min Li. "Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/348326

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1276.26065
MathSciNet: MR3035385
Digital Object Identifier: 10.1155/2013/348326

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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