lipschitzienne.py

Created by alten01

Created on December 11, 2024

438 Bytes

Mq g est lipschitzienne de rapport
L<1 sur [0;1]
g(x)=...
g'(x)=...
g''(x)=...

g est derivable sur I

g' est mono croiss car g''(x)>0
On a alors
g'(a)<=g'(x)<=g'(b)
Soit abs(g'(x))<=g'(b)

g' est mono decroiss car g''(x)<0
On a alors
g'(b)<=g'(x)<=g'(a)
Soit abs(g'(x))<=g'(a)

donc g est lip de cst L=g'(a)oub

si L<1 on dit que g est contrancte



critere darret 
pour tout n app N
abs(xn-xbar)<=L^nabs(x0-xbar)

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