Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906. Jensen's inequality generalizes the statement that the secant line of a convex function lies above the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function. For t belongs to [0,1], there exists: $f(t x_1 + (1-t) x_2) <= t f(x_1) + (1-t) f(x_2)$