It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental arithmetic-geometric-harmonic mean inequality and Sierpinski's inequality in terms of the means and variance of positive real numbers. We also obtain some inequalities involving third and fourth central moments of real numbers.
"Means, moments and Newton's inequalities." Rocky Mountain J. Math. 49 (5) 1667 - 1677, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1667