Rocky Mountain Journal of Mathematics

Means, moments and Newton's inequalities

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

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Abstract

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

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

Dates
First available in Project Euclid: 19 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1568880096

Digital Object Identifier
doi:10.1216/RMJ-2019-49-5-1667

Mathematical Reviews number (MathSciNet)
MR4010578

Zentralblatt MATH identifier
07113704

Subjects
Primary: 60E15: Inequalities; stochastic orderings

Keywords
arithmetic mean geometric mean moments Newton's identities

Citation

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. https://projecteuclid.org/euclid.rmjm/1568880096


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