Jensen's inequality

Jensen's inequality is a mathematical concept that relates the value of a convex (curved upward) function applied to an average, compared to applying the function before averaging. In simple terms, for a convex function, the function of the average is less than or equal to the average of the function’s values. Conversely, for a concave (curved downward) function, the function of the average is greater than or equal to the average of the function’s values. This inequality helps analyze how the "shape" of a function affects the relationship between averages before and after the function is applied.