MHB Fixed Point Theorem & Contractive Maps

[ozkan12]

Please give an example of contractive map which have fixed point...I search but I didnt find

 

[Fallen Angel]

Hi,

A trivial example is the constant real function 1.

 

[Nono713]

Another trivial example is the map $x \mapsto kx$ for $0 \leq k < 1$ over, say, the reals. It has an obvious fixed point: zero.