Let f be q function defined from [a,b] to [a,b] such that for every (x,t) in [a,b]^2:
l f(x)-f(t) l < l x-t l
1- prove that f is continuous on [a;b]
2-prove that f accepts a steadfast point in [a,b]
The Attempt at a Solution
Should i try to use the definition of a limit to show that f is continuous?
If not can someone give me headers. Thank you very much