论文标题
在对数平均值和平均不等式链的界限上
On bounds of logarithmic mean and mean inequality chain
论文作者
论文摘要
对数平均值的上限是由算术平均值和几何平均值的凸组合给出的。另外，对数平均值的下限是由算术平均值和几何平均值的几何桥给出的。在本文中，我们研究对数平均值的界限。我们给对数平均值的基本不平等而给操作员的不平等和规范不平等。我们给出了苍鹭均值单位不变标准的参数的单调性，并将其作为对数平均值单位不变标准的上限。我们研究了苍鹭平均值，亨氏平均值，二项式平均值和莱默（Lehmer）的单位规范的顺序。最后，我们给出了一个新的平均不平等链，以应用点不平等。
An upper bound of the logarithmic mean is given by a convex combination of the arithmetic mean and the geometric mean. In addition, a lower bound of the logarithmic mean is given by a geometric bridge of the arithmetic mean and the geometric mean. In this paper, we study the bounds of the logarithmic mean. We give operator inequalities and norm inequalities for the fundamental inequalities on the logarithmic mean. We give monotonicity of the parameter for the unitarily invariant norm of the Heron mean, and give its optimality as the upper bound of the unitarily invariant norm of the logarithmic mean. We study the ordering of the unitarily invariant norms for the Heron mean, the Heinz mean, the binomial mean and the Lehmer mean. Finally, we give a new mean inequality chain as an application of the point-wise inequality.
