不动点数列-数学.pdf
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雷 波
( , 528200)
( 本讲适合高中) 2an- 1 + 1( n 1) . { an }
, f ( x ) D , a = .
n
x 0 I D , f ( x 0 ) = x 0 , x 0 ( 1999, )
f ( x ) , ( x 0 , x 0 ) y = f ( x ) : x = 2x + 1, x = - 1.
. / 0 an + 1= 2( an- 1 + 1) .
( Brouwer) . , { a + 1} a + 1= 2
n 1
, 2 .
. n- 1 n n
a + 1= 2 @ 2 = 2 , a = 2 - 1.
n n
. 2 { a } ,
n
1 a1 = 10, ak + 1 = 10 ak ( k = 1, 2, ,) .
an .
1 { an } an + 1 = p an + q
(p I {0, 1}) , x 0 f ( x ) = px + q : b = lg a . b = 1 b + 1.
k k k + 1 2 k
, a - x = p ( a - x ) .
n+ 1 0 n 0 1
: x 0 f ( x ) = p x + q x = 2 x + 1, x = 2.
, , 1
b - 2= ( b - 2) .
x 0 = p x 0
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