Sharp bounds for power mean in terms of generalized Heronian mean
Summary: For \(1 < r < +\infty\), we find the least value \(\alpha\) and the greatest value \(\beta\) such that the inequality \(H_{\alpha}(a, b) < A_r(a, b) < H_{\beta}(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\). Here, \(H_{\omega}(a, b)\) and \(A_r(a, b)\) are the generalized Heronian and the power means of two positive numbers \(a\) and \(b\), respectively.
scientific article; zbMATH DE number 5930770