MHB Fixed Point Theorem & Contractive Maps

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.
 

Thread 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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