Fixed Point Theorem & Contractive Maps

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ozkan12
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Please give an example of contractive map which have fixed point...I search but I didnt find
 
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Hi,

A trivial example is the constant real function 1.
 
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.
 

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