Vornicu-Schur Inequality
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
Let be real numbers, and let
. Then if
then the following inequality is true
References
- Vornicu, Valentin; Olimpiada de Matematica... de la provocare la experienta; GIL Publishing House; Zalau, Romania.</ref>