In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number 0 ≤ k < 1 {\displaystyle 0\leq k<1} such that for all x and y in M, d ( f ( x ) , f ( y ) ) ≤ k d ( x , y ) . {\displaystyle d(f(x),f(y))\leq k\,d(x,y).} The smallest such value of k is called the Lipschitz constant of f.
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number 0 ≤ k < 1 {\displaystyle 0\leq k<1} such that for all x and y in M, d ( f ( x ) , f ( y ) ) ≤ k d ( x , y ) . {\displaystyle d(f(x),f(y))\leq k\,d(x,y).} The smallest such value of k is called the Lipschitz constant of f.
Source: Wikipedia "Contraction mapping" · CC BY-SA 4.0
Share this article: X · Bluesky