Difference between revisions of "Vornicu-Schur Inequality"
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==Theorem== | ==Theorem== | ||
| − | In | + | In 2007, Romanian mathematician [[Valentin Vornicu]] showed that a generalized form of Schur's inequality exists: |
Consider <math>a,b,c,x,y,z \in \mathbb{R}</math>, where <math>a \ge b \ge c</math>, and either <math>x \geq y \geq z</math> or <math>>z \geq y \geq x</math>. Let <math>k \in \mathbb{Z}^{+}</math>, and let <math>f:\mathbb{R} \rightarrow \mathbb{R}_{0}^{+}</math> be either [[convex function|convex]] or [[monotonic]]. Then, | Consider <math>a,b,c,x,y,z \in \mathbb{R}</math>, where <math>a \ge b \ge c</math>, and either <math>x \geq y \geq z</math> or <math>>z \geq y \geq x</math>. Let <math>k \in \mathbb{Z}^{+}</math>, and let <math>f:\mathbb{R} \rightarrow \mathbb{R}_{0}^{+}</math> be either [[convex function|convex]] or [[monotonic]]. Then, | ||
Revision as of 14:38, 30 March 2008
The Vornicu-Schur' refers to a generalized version of Schur's Inequality.
Theorem
In 2007, Romanian mathematician Valentin Vornicu showed that a generalized form of Schur's inequality exists:
Consider 
, where 
, and either 
or 
. Let 
, and let 
be either convex or monotonic. Then,
The standard form of Schur's is the case of this inequality where 
, 
, 
, 
, and 
.
External Links
- A full statement, as well as some applications can be found in this article.
References
- Vornicu, Valentin; Olimpiada de Matematica... de la provocare la experienta; GIL Publishing House; Zalau, Romania.</ref>
