Sentence examples for be a real order from inspiring English sources

Let be a real linear space, and let be a real order complete PL space.

Proof Let X be a real ordered Banach space, let A be a γ-ordered non-extended mapping and a comparison mapping M be a ( α A, λ ) -ANODM mapping, then ( A + λ M ) ( X ) = X for α A, λ > 0. It is follows that ( A + λ ω ( ω M ) ) ( X ) = X for α A, λ ω > 0. Therefore, ωM is a ( α A, λ ω ) -ANODM mapping by Lemma 2.6.

Lemma 3.4 Let X be a real ordered Banach space.

Let X be a real ordered Banach space.

Proof Let X be a real ordered Banach space, and let X × X be an ordered product Banach space.

Definition 2.6 Let X be a real ordered Banach space, and let F : X × X → X be a mapping.

Allow X to be a real ordered Banach space and C a normal cone having the normal constant (lambda_{C}).

Proof Let X be a real ordered Banach space, and let the resolvent operator J M, λ A of M exist.

Let X be a real ordered Banach space, let A : X → X be a single-valued mapping, and let M : X → 2 X be a set-valued mapping.

Definition 2.5 Let X be a real ordered Banach space, A : X → X be a single-valued mapping, and M X X → 2 X be a set-valued mapping.

Let X be a real ordered Banach space, let B : X → X be a mapping, and let I be an identity mapping on X.