Rocky Mountain Journal of Mathematics

Means, moments and Newton's inequalities

R. Sharma, A. Sharma, R. Saini, and G. Kapoor

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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.

Article information

Rocky Mountain J. Math., Volume 49, Number 5 (2019), 1667-1677.

First available in Project Euclid: 19 September 2019

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings

arithmetic mean geometric mean moments Newton's identities


Sharma, R.; Sharma, A.; Saini, R.; Kapoor, G. Means, moments and Newton's inequalities. Rocky Mountain J. Math. 49 (2019), no. 5, 1667--1677. doi:10.1216/RMJ-2019-49-5-1667.

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