# M´emoire d’initiation `a la recherche

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i

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v∈V

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k+1

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k:1

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k:1

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(8)

n

n

|x|x

+

TT(u(x))(u(y))

|λ|λ

|λ|λ

+

+

−1

−1

−1

n

d

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3

2

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0

0

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0

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1

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2

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## Applications du th´ eor` eme du point fixe de Brouwer

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n

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i

i∈N

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i∈N

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−i

bi∈Ai

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−i

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i

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i

### ) =

1+xiP(ai)+[gi(ai,x−i)−gi(x)]+

bi∈Ai[gi(bi,x−i)−gi(x)]+

+

1

N

i

i

ai∈Ai

i

i

### ) =

P

ai∈Aixi(ai)+[gi(ai,x−i)−gi(x)]+ 1+P

bi∈Ai[gi(bi,x−i)−gi(x)]+

### =

1+

P

ai∈Ai[gi(ai,x−i)−gi(x)]+ 1+P

bi∈Ai[gi(bi,x−i)−gi(x)]+

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bi∈Ai

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−i

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## References

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