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An optimal double inequality between geometric and identric means. (English) Zbl 1247.26040
Summary: 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 ab. Here, G(a,b), and I(a,b) denote the geometric, and identric means of two positive numbers a and b, respectively.
26D15Inequalities for sums, series and integrals of real functions
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