On a Mixed Arithmetic-Mean, Geometric-Mean, Harmonic-Mean Inequality

A mixed arithmetic-mean, geometric-mean inequality was conjectured by F. Holland and proved by K. Kedlaya. In this note, we prove a mixed arithmetic-mean, harmonic-mean inequality and a mixed geometric-mean, harmonic-mean, and a more extended inequality: a mixed arithmetic-mean, geometric-mean, harmonic-mean inequality.