Means, moments and Newton's inequalities (Q2326039)

In this paper, the authors study the arithmetic-geometric-harmonic mean inequality and Sierpinski's inequality in terms of means and variance of positive real numbers. They show that the Newton inequalities and the related Maclaurin inequalities provide several refinements of the above inequalities in terms of the means and variance of positive real numbers. Furthermore, some inequalities involving third and fourth central moments of real numbers are derived and proved similarly.