Glaeser's Inequality on an Interval
Mathematical Association of America
"Glaeser's Inequality" is a theorem of elementary calculus which states that if a function f is non-negative on R and has continuous second derivative bounded by M, then the first derivative satisfies |f'(x)|<=sqrt(2Mf(x)) at every point x. It is easy to find counterexamples if we change the domain R to an arbitrary interval, but I will present an analogous pointwise inequality for functions on an interval, which specializes to Glaeser's inequality as a limiting case.
Analysis | Mathematics
Adam Coffman and Yifei Pan (2010).
Glaeser's Inequality on an Interval. Presented at Mathematical Association of America, Pittsburgh, PA.