Sentence examples for be a complete ordered from inspiring English sources

Theorem 2 Let ( X, d, ⪯ ) be a complete ordered metric space.

Theorem 4.2 Let ( X, ⪯, ρ ) be a complete ordered modular function space.

Corollary 1 Let ( X, d, ⪯ ) be a complete ordered metric space.

Let ( X, ⪯, d ) be a complete ordered b-metric space and A and B be closed subsets of X.

Theorem 3.5 Let ( X, ⪯, ρ ) be a complete ordered modular function space and S, T, I, and J continuous self-maps on X ρ.

Theorem 3.3 Let ( X, d, ⪯ ) be a complete ordered metric space, and let f, g, T, S X X → X be four mappings.

Then ( X, d ) is a complete ordered cone metric space over a non-normal solid cone.

It is clear that ( X, d ) is a complete metric space and ( X, d, ⪯ ) is a complete ordered metric space if x ⪯ y whenever x ( t ) ≤ y ( t ) for all t ∈ [ a, b ].

Define the order ≤ on M by f ≤ g if and only if f ( t ) ≤ g ( t ) for all t ∈ I. Then ( M, ≤, d ) is a complete ordered metric space, where d ( f, g ) = sup t ∈ I | f ( t ) − g ( t ) |.

Recently, Vasile Berinde and Marin Borcut [39] extended and generalized the results of [21] to the case of a contractive operator F : X × X × X → X, where X is a complete ordered metric space.

Let ( X, d, ⪯ ) be a complete partially ordered 2-metric space.