Karamata's inequality [SEP] named after
Karamata's inequality
In mathematics, Karamata's inequality, named after Jovan Karamata, also known as the majorization inequality, is a theorem in elementary algebra for convex and concave real-valued functions, defined on an interval of the real line. It generalizes the discrete form of Jensen's inequality, and generalizes in turn to the concept of Schur-convex functions.
Statement of the inequality.
Let be an interval of the real line and let denote a real-valued, convex function defined on . If and
- Hölder's inequality
- Jackson's inequality
- Jensen's inequality
- Khabibullin’s conjecture on integral inequalities
- Kantorovich inequality
- Karamata's inequality
- Korn's inequality
- Ladyzhenskaya's inequality
- Landau–Kolmogorov inequality
- Lebedev–Milin inequality
- Lieb–Thirring inequality
- Littlewood's 4/3 inequality
- Markov brothers' inequality
- Mashreghi–Ransford inequality
- Max–min inequality
- Minkowski's inequality
- Poincaré inequality
- Popoviciu's inequality
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