nevermind i think i figured it out. When x and y are close to 0 then then it would be impossible to fix a k.
For Lipschitz condition:
for constant k on [a,b] if there is a constant k such that for all x,y in [a,b]
|Tx -Ty| less than or equal to k|x-y|
I have to show if:
f(t,x)=|x|^(1/2)
satisfies the condition
I think it would but i am having trouble proving this. Is there a way to find a minimum value k such that all Tx-Ty satisfy this condition?