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2 Journal of Applied Analysis

2 2013

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Optimal bounds for logarithmic and identric means in terms of generalized centroidal mean

Zhang T, Xia W, Chu Y, Wang G

Journal of Applied Analysis

2013

Vol. 19, nr 1

141--152

Best possible upper and lower bounds are given for the logarithmic and identric mean values in terms of the generalized centroidal mean.

An optimal double inequality between logarithmic and generalized logarithmic means

Jiang Y., Long B., Chu Y.

Journal of Applied Analysis

2013

Vol. 19, nr 2

271--182

In this paper, we answer the question: for any q > 0 with q ≠ 1, what are the greatest value p1= p1(q) and the least value p2= p2(q) such that the double inequality Lp1(a, b) < [L(aq, bq)]1/q < Lp2(a, b) holds for all a, b > 0 with a ≠ b? Here L(a, b) and Lp(a, b) are the logarithmic and pth generalized logarithmic means of a and b, respectively.