Sentence examples for be an ordered normed from inspiring English sources

Theorem 1 If the underlying cone of an ordered tvs is solid and normal, then such tvs must be an ordered normed space.

However, it should be noted that an old result (see, e.g., [3]) shows that if the underlying cone of an ordered tvs is solid and normal, then such tvs must be an ordered normed space.

However, it should be noted that an old result shows that if the underlying cone of an ordered tυs is solid and normal, then such tυs must be an ordered normed space.

However, it should be noted that an old result shows that if the underlying cone of an ordered tvs is solid and normal, then such tvs must be an ordered normed space.

Let X be a nonempty set, and let L be an ordered normed space with a cone H. (i) The family P = { p α : X 2 → L, α ∈ A }, A -index set, is said to be a P -family of cone pseudometrics on X ( P -family for short) if the following three conditions hold:  .

Let L be an ordered normed space with a normal solid cone H, and let ( X, P ) be a Hausdorff cone uniform space with a cone H. (i) The family J = { J α : X 2 → L, α ∈ A } is said to be a J -family of cone pseudodistances on X ( J -family on X for short) if the following three conditions hold:  .

It is clear that each cone H ⊂ L defines, by virtue of " a ⪯ H b  iff  b − a ∈ H ", an order of L under which L is an ordered normed space with a cone H.

In this case E is called an ordered normed vector space.

[10] Let be an ordered Banach (normed) space.

Let E be an ordered Banach (normed) space.

Let be a subset of an ordered normed space, an increasing mapping, and.