Bourguignon's Inequality

Bourguignon's Inequality is a mathematical statement that relates the way a function's values change over an interval to the change in its average rate of change, accounting for the function’s curvature. In simple terms, it provides bounds on how much the function’s overall increase or decrease can differ from its average slope, considering the function's second derivative (curvature). This inequality is useful in analysis to estimate the behavior of functions, especially when precise calculations are complicated, by giving an understanding of how the function’s shape influences its overall variation.