A lower bound for ratio of power means
Summary: Let \(n\) and \(m\) be natural numbers. Suppose that \(\{a_i\}_{i=1}^{n+m}\) is an increasing, logarithmically convex, and positive sequence. Denote the power mean \(P_n(r)\) for any given positive real number \(r\) by \(P_{n}(r)=((1/n)\sum_{i=1}^{n} a_i^r)^{1/r}\). Then \({P_n(r)}/{P_{n+m}(r)}\geq{a_n}/{a_{n+m}}\). The lower bound is the best possible.
scientific article; zbMATH DE number 2168597