科研之友
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摘要
For x, y > 0 with x not equal y, let L = L(x, y), I = I(x, y), A = A(x, y), G = G(x, y), A(r) = A(1/r)(x(r), y(r)) denote the logarithmic mean, identric mean, arithmetic mean, geometric mean and r-order power mean, respectively. We find the best constant p, q > 0 such that the inequalities A(p)(1/(3p))G(1-1/(3p)) < L < A(q)(1/(3q))G(1-1/(3q)), A(p)(2/(3p))G(1-2/(3p)) < I < A(q)(2/(3q))G(1-2/(3q)) hold, respectively. From them some new inequalities for means are derived. Lastly, our new lower bound for the logarithmic mean is compared with several known ones, which shows that our results are superior to others.
- 出版日期2013
