The Vornicu-Schur Inequality is a generalization of Schur's Inequality discovered by the Romanian mathematician Valentin Vornicu.
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
- Vornicu, Valentin; Olimpiada de Matematica... de la provocare la experienta; GIL Publishing House; Zalau, Romania.