Contraction Mappings <Back to Last Page>     <Full Glossary>

Definition of Contraction Mappings: Given a metric space S with distance measure d(), and T:S->S mapping S into itself, T is a contraction mapping if for some b ('b') in the range (0,1), d(Tx,Ty) is less than or equal to b*d(x,y) for all x and y in S.

One often abbreviates the phrase 'contraction mapping' by saying simply that T is a contraction.

The function resulting from the applications of a contraction could slope the opposite way of the original function as long as it is less steeply sloped.

A standard way to prove that an operator T is a contraction is to prove that it satisfies Blackwell's conditions (Econterms)

Terms related to Contraction Mappings:

• Blackwell's conditions
• Metric space

About.Com Resources on Contraction Mappings:
None

Writing a Term Paper? Here are a few starting points for research on Contraction Mappings:

Books on Contraction Mappings:
None

Journal Articles on Contraction Mappings:
None

<Return to Main Page>