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Preprint
Generalizations of Popoviciu's inequality
arXiv.org
20 Mar 2008
Abstract
We establish a general criterion for the validity of inequalities of the
following form: A certain convex combination of the values of a convex function
at n points and of its value at a weighted mean of these n points is always
greater or equal to a convex combination of the values of the function at some
other weighted means of these points. Here, the left hand side contains only
one weighted mean, while the right hand side may contain as many as possible,
as long as there are finitely many. The weighted mean on the left hand side
must have positive weights, while those on the right hand side must have
nonnegative weights.
The most prominent example of such kind of inequalities, Popoviciu's
inequality in its most general form, follows from the general criterion. As
another application, a result by Vasile Cirtoaje is sharpened.
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Details
- Title
- Generalizations of Popoviciu's inequality
- Creators
- Darij Grinberg
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862240004721