Sentence examples for there exists a nonnegative number from inspiring English sources

Let ( X, d ) be a complete metric space and T : X → C B ( X ) be a k-contraction; that is, there exists a nonnegative number k < 1 such that H ( T x, T y ) ≤ k d ( x, y ) for all x, y ∈ X, where C B ( X ) is the class of all nonempty closed bounded subsets of X.

For all (kgeq0), there exists a nonnegative number (m_{k}) satisfying (9).

For all (kgeq0), there exists a nonnegative number m satisfying (3.2).

Assume that there exists a nonnegative number such that for any, (3.50).

Assume that there exists a nonnegative number such that for any with, (3.44).

Assume that there exists a nonnegative number γ < 1 such that d ( T x, T y ) ≤ γ d ( x, y ) for all x, y ∈ X.

A mapping T : C → C is said to be asymptotically nonexpansive if for each n ≥ 1, there exists a nonnegative real number k n satisfying lim n → ∞ k n = 1 such that ∥ T n x − T n y ∥ ≤ k n ∥ x − y ∥, ∀ x, y ∈ C ; when k n ≡ 1, T is called nonexpansive.

By the definition of the matrix, for each positive number there exists a nonnegative integer such that (5.12).

for all nonnegative integers n or there exists a nonnegative integer such that.

Then for each given element, either (1.2). for all nonnegative integers n or there exists a nonnegative integer such that.

Without loss of generality, let us assume that there exists a nonnegative real number such that, for all.