Is f a Continuous Function with a Fixed Point on [a,b]?

[mtayab1994]

Homework Statement

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

 

[jbunniii]

Yes, for part 1, use the definition of continuity.

For part 2, I assume "accepts a steadfast point" means "has a fixed point." If so, consider the function defined by f(x) - x.