I am reading a proof in a textbook and the author uses an assumption of "convexity modulus" for a function $l$ which states:
$$ l(u)+l(v)-l\left(\frac{u+v}{2}\right) \geq C |u-v|^2 $$
for some $C > 0$.
Is this standard terminology?
Asked
Active
Viewed 55 times
1
-
To check if it holds for $l(u)=u^2$ is straightforward. About the standard terminology, I have never heard of the convexity modulus or midpoint-convexity modulus, but it is a fairly natural generalization of $\frac{f(u)-f(v)}{|u-v|}$. – Jack D'Aurizio Oct 15 '18 at 15:14