Research Article
Open Access
Inequalities involving the mean and the standard deviation of nonnegative real numbers
- Oscar Rojo1Email author
Journal of Inequalities and Applications20062006:43465
https://doi.org/10.1155/JIA/2006/43465
© Oscar Rojo. 2006
Received: 22 December 2005
Accepted: 21 September 2006
Published: 8 November 2006
Abstract
Let
and
be the mean and the standard deviation of the components of the vector
, where
with
a positive integer. Here, we prove that if
, then
for
. The equality holds if and only if the
largest components of
are equal. It follows that
is a strictly increasing sequence converging to
, the largest component of
, except if the
largest components of
are equal. In this case,
for all
.
Authors’ Affiliations
(1)
Departamento de Matemáticas, Universidad Católica del Norte
References
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Copyright
© Oscar Rojo. 2006
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
