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2014 Sharp Geometric Mean Bounds for Neuman Means
Yan Zhang, Yu-Ming Chu, Yun-Liang Jiang
Abstr. Appl. Anal. 2014: 1-6 (2014). DOI: 10.1155/2014/949815


We find the best possible constants α1,α2,β1,β2[0,1/2] and α3,α4,β3,β4[1/2,1] such that the double inequalities G(α1a+(1-α1)b,α1b + (1-α1)a)<NAG(a,b)<G(β1a + (1-β1)b,β1b+(1-β1)a), G(α2a+(1-α2)b,α2b + (1-α2)a)<NGA(a,b)<G(β2a + (1-β2)b,β2b+(1-β2)a), Q(α3a+(1-α3)b,α3b + (1-α3)a)<NQA(a,b)<Q(β3a + (1-β3)b,β3b+(1-β3)a), Q(α4a+(1-α4)b,α4b + (1-α4)a)<NAQ(a,b)<Q(β4a + (1-β4)b,β4b+(1-β4)a) hold for all a,b>0 with ab, where G, A, and Q are, respectively, the geometric, arithmetic, and quadratic means and NAG, NGA, NQA, and NAQ are the Neuman means.


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Yan Zhang. Yu-Ming Chu. Yun-Liang Jiang. "Sharp Geometric Mean Bounds for Neuman Means." Abstr. Appl. Anal. 2014 1 - 6, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023379
MathSciNet: MR3208577
Digital Object Identifier: 10.1155/2014/949815

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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