Sentence examples for mappings it holds from inspiring English sources
For any sequence of mappings, it holds that (2.12).
Suppose that S, T are two self-mappings of a multiplicative metric space ( X, d ) ; S, T are called commutative mappings if it holds that for all x ∈ X, S T x = T S x.
Suppose that S, T are two self-mappings of a multiplicative metric space ( X, d ) ; S, T are called weak commutative mappings if it holds that for all x ∈ X, d ( S T x, T S x ) ≤ d ( S x, T x ).
β (shortly, β-condensing) if for every Ω ⊂ X such that β ( F , it holds that Ω is relatively compact. A family of mappings G : X × [ 0, 1 ] ⊸ E with compact values is called β-condensing if for every Ω ⊂ X such that β ( G ( Ω × [ 0, 1 ] ) ) ≥ β , it holds that Ω is relatively compact.
A representation of a left reversible semigroup as Lipschitzian mappings on with Lipschitz constants is said to be a contractive (resp., asymptotically contractive) semigroup on if it holds the uniform Lipschitzian condition (resp., ) on the Lipschitz constants.
"Whatever the future holds, it holds".
