# Contraction-mapping principle

From Encyclopedia of Mathematics

One of the fundamental statements in the theory of metric spaces on the existence and uniqueness of a fixed point of a set under a special ( "contractive" ) mapping of the set into itself. See Contracting-mapping principle.

**How to Cite This Entry:**

Contraction-mapping principle.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Contraction-mapping_principle&oldid=12160