Sentence examples for be an ordered real from inspiring English sources

Let X be an ordered real Banach space with a normal order cone.

Let H be an ordered real Hilbert space with an ordering given by a closed cone P and suppose that the gradient Φ ′ : H → H of a given functional Φ ∈ C 1 ( H, R ) has the expression Φ ′ = I − A. Obviously, the critical points of the functional Φ are the fixed points of the operator A, and vice versa.

The real Banach space X endowed with the ordered relation ≤ defined by C is called an ordered real Banach space.

Let be an ordered parameter group of nonnegative real numbers.

Let ([x, y, z]) be an ordered parameter group of nonnegative real numbers.

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

Theorem 4.1 Let X be a real ordered Banach space, let P be a normal cone with normal constant N in X, let ≤ be an ordered relation defined by the cone P, and let the operator ⊕ be an XOR operator.

Lemma 3.5 Let X be a real ordered Banach space, let P be a normal cone with normal constant N in X, let ≤ be an ordered relation defined by the cone P, let the operator ⊕ be an XOR operator.

Lemma 2.10 Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a zero θ, a normal cone P, a normal constance N of P and a partial ordered relation ≤ defined by the cone P. Let X × X be an ordered product Banach space.

Lemma 3.1 Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a zero θ, a normal cone P, a normal constance N of P and a partial ordered relation ≤ defined by the cone P, and let X × X be an ordered product Banach space.

Theorem 3.2 Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a zero θ, a normal cone P, a normal constance N of P and a partial ordered relation ≤ defined by the cone P, and let X × X be an ordered product Banach space.