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Contraction

• Definition: Let f: S -> S be a function from a metric space (S, d) into itself. The function f is called a contraction of S if there is a positive number z < 1 (called a contraction constant), such that d(f(x), f(y)) <= zd(x, y) for all x, y in S.

  Source: Mathematical Analysis, second edition by Tom M. Apostol