This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 2.123 By the Banach fixed point theorem, for every , there exists such that ( ) = . Choose any . ( , ) = ( ( ) , ( )) ( ( ) , ( )) + ( ( ) , ( )) ( , ) + ( ( ) , ( )) (1 ) ( , ) ( ( ) , ( )) ( , ) ( ( ) , ( )) (1 ) as . Therefore . 2.124 1. Let x be a fixed point of . Then x satisfies x = ( ) x + c = x x + which implies that x = . 2. For any x 1 , x 2 ( x 1 ) ( x 2 ) = ( )( x 1 x...
View Full Document
- Fall '10