An optimal double inequality between geometric and identric means |
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| Authors: | Miao-Kun WangZi-Kui Wang Yu-Ming Chu |
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| Affiliation: | a Department of Mathematics, Huzhou Teachers College, Huzhou 313000, Chinab Department of Mathematics, Hangzhou Normal University, Hangzhou 310018, China |
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| Abstract: | ![]()
We find the greatest value p and least value q in (0,1/2) such that the double inequality G(pa+(1−p)b,pb+(1−p)a)<I(a,b)<G(qa+(1−q)b,qb+(1−q)a) holds for all a,b>0 with a≠b. Here, G(a,b), and I(a,b) denote the geometric, and identric means of two positive numbers a and b, respectively. |
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| Keywords: | Geometric mean Identric mean Inequality |
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