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Unformatted text preview: 2) Let ( X , d ) be a complete metric space and T be a contraction mapping on X with modulus (0, 1). Let x * be the unique fixed point of T . Let x X , and let n . Then by the Triangle Inequality, *). , ( ) , ( *) , ( 1 1 x x T d x T x T d x x T d n n n n + + + Since T is a contraction, we also have *). , ( *) , ( *) , ( 1 1 x x T d Tx x T d x x T d n n n = + + Thus, ). , ( 1 1 *) , ( ) , ( *) , ( ) 1 ( *). , ( ) , ( *) , ( 1 1 1 x T x T d x x T d x T x T d x x T d x x T d x T x T d x x T d n n n n n n n n n n + + + +...
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 Spring '10
 Feigenbaum
 Macroeconomics

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