Inequalities
Note on Jensen's Inequality [Link]:
This is a brief note on the discrete version of Jensen's inequality, a fundamental result in convex analysis that relates the value of a convex function at a finite convex combination of points to the corresponding convex combination of their function values. This note introduces the basic notions of convex sets, convex functions, and strictly convex functions, states the discrete Jensen's inequality together with its equality condition, and provides a proof by mathematical induction.