I have a function that is differentiable on [a,b] and I am trying to figure out which scenario is more restrictive:
a) the function is a Lipschitz function with a Lipschitz constant L in (0,1)
b) the absolute value of f'(x) is less than one for all x in [a,b]
Answer: (a) is more restrictive.
I claim that (a) can imply (b).
Suppose (a) holds. f(x) is a ...
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