Statement 1:
A function $f$ satisfies a Lipschitz condition in the rectangular region $D$ if there is a positive real number $L$ such that $|f(t, u) - f(t, v)| \leq L|u - v|$ for all $(t,u) \in D$ and $(t, v) \in D$.
Statement 2:
There is a finite, positive, real number $L$ such that $|\frac{d}{dy}f(t, y)| \leq L$ for all $(t,y) \in D$.
Is this statement stronger than (i.e., more restrictive then), equivalent to or weaker than (i.e., less restrictive than) statement 1? Justify your answer.
My view:
I would say the statements are equivalent the max 'slope' for any two points in statement 1 won't exceed the max slope in statement 2.