Sentence examples for a uniform contraction from inspiring English sources

so is a uniform contraction.

Therefore is a uniform contraction.

(ii) is a uniform contraction on.

Therefore, J1 is a uniform contraction.

(ii) K N is a uniform contraction on X.  .

K N is a uniform contraction on X.

More surprisingly, even a simplistic uniform contraction of the model can in many cases produce higher GDT_TS (Fig. 2; Section 3.3).

If condition (a) is changed to ϕ ( d ( g ( x ), g ( y ) ) ) ≤ k d ( x, y ) for all  x, y ∈ X, then g is a uniform local contraction on ( X, d ).

If this condition is satisfied for some ε > 0 independent of x then g is said to be a uniform local contraction.

This is because condition (b) now implies that there exists δ > 0 such that d ( x, y ) < δ ⇒ ϕ ( d ( g ( x ), g ( y ) ) ) ≤ k d ( x, y ) ≤ ϕ ( c d ( x, y ) ). Remark 2.5 If g : X → X is onto and satisfies the following expansive type condition: there exists k ∈ ( 0, 1 ) such that d ( g ( x ), g ( y ) ) ≥ k − 1 ϕ ( d ( x, y ) ) for all  x, y ∈ X, then g − 1 is a uniform local contraction on ( X, d ).

One can investigate it by the uniform contraction mapping principle as in [23].