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The quest may be for references but I want to know if there is a simple way to prove the Brouwer fixed point theorem!

That is if a function $f:\bar{B}\to\bar{B}$ is continuous then $f$ admits one fixed point!

The answer for the is a real analysis exercise and it also holds for any interval compact!

The proof is related with Schauder fixed-point theorem?

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    The number of exclamation marks probably means that you're very excited! So I'm sure you have looked at the extensive [Wikipedia page](http://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem)! Why do the references and proofs given there not answer your question? @Jim: och, you beat me to it! :)2012-03-28

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There is a book proof using Sperner's Lemma which is (very!) elegant and (IMO) simple.

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    @MarianoSuárez-Alvarez: Thanks! Corrected :-)2012-03-28