A best possible double inequality for power mean
Summary: We answer the question: for any \(p, q \in \mathbb R\) with \(p \neq q\) and \(p \neq -q\), what are the greatest value \(\lambda = \lambda(p, q)\) and the least value \(\mu = \mu(p, q)\), such that the double inequality \(M_\lambda(a, b) < \sqrt{M_p(a, b) M_q(a, b)} < M_\mu(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\)? Where \(M_p(a, b)\) is the \(p\)th power mean of two positive numbers \(a\) and \(b\).
scientific article; zbMATH DE number 6169895
scientific article