Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions?
2026-04-07 16:13:02.1775578382
Convexity defined by Karamata inequality
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Wikipedia says that Jensen's inequality is a special case of Karamata's inequality. Hence, if a function satisfies Karamata's inequality, it satisfies also Jensen's inequality and, thus, is convex.