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2013 Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means
Fan Zhang, Yu-Ming Chu, Wei-Mao Qian
J. Appl. Math. 2013: 1-7 (2013). DOI: 10.1155/2013/582504

Abstract

We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b)+(1-α1)H(a,b)<A(a,b)<β1M(a,b)+(1-β1)H(a,b), α2M(a,b)+(1-α2)H-(a,b)<A(a,b)<β2M(a,b)+(1-β2)H-(a,b), and α3M(a,b)+(1-α3)He(a,b)<A(a,b)<β3M(a,b)+(1-β3)He(a,b) hold for all a,b>0 with ab, where M(a,b), A(a,b), He(a,b), H(a,b) and H-(a,b) denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively.

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Fan Zhang. Yu-Ming Chu. Wei-Mao Qian. "Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/582504

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950758
MathSciNet: MR3147875
Digital Object Identifier: 10.1155/2013/582504

Rights: Copyright © 2013 Hindawi

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