Difference between revisions of "Vornicu-Schur Inequality"
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− | *Vornicu, Valentin; ''Olimpiada de Matematica... de la provocare la experienta''; GIL Publishing House; Zalau, Romania. | + | *Vornicu, Valentin; ''Olimpiada de Matematica... de la provocare la experienta''; GIL Publishing House; Zalau, Romania. |
− | + | [[Category:Algebra]] | |
− | [[Category: | + | [[Category:Inequalities]] |
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Latest revision as of 16:58, 29 December 2021
The Vornicu-Schur Inequality is a generalization of Schur's Inequality discovered by the Romanian mathematician Valentin Vornicu.
Statement
Consider real numbers such that
and either
or
. Let
be a positive integer and let
be a function from the reals to the nonnegative reals that is either convex or monotonic. Then
Schur's Inequality follows from Vornicu-Schur by setting ,
,
,
, and
.
The most widely used form of Vornicu-Schur is in the case ,
, when we have for real numbers
and nonnegative real numbers
that if
then
References
- Vornicu, Valentin; Olimpiada de Matematica... de la provocare la experienta; GIL Publishing House; Zalau, Romania.