Sentence examples for ordered approximation from inspiring English sources

As applications we prove several existence theorems for best ordered approximation.

Then f has a best ordered approximation on K. Equal contributors.

Hence s ∗ is a best ordered approximation of f on K. □.

Similarly to the proof of Theorem 4.1, the fixed point of T f is a best ordered approximation of f on K. □.

As applications of the fixed point theorems proved in previous section, in this section, we extend the concept of best approximation from metric spaces to ordered metric spaces and give some best ordered approximation theorems.

An element u ∈ K is called an extended best ordered approximation of f on K, if it satisfies d X ( u, f ( u ) ) ∈ Min { d X ( s, f ( u ) ) : s ∈ K }, where Min { d X ( s, f ( u ) ) : s ∈ K } is the set of minimal elements of the set { d X ( s, f ( u ) ) : s ∈ K } with respect to the ordering ≽ X on X.

In a first-order approximation the polymers in solution can consequently be approximated by rigid rods.

Solid line: first-order approximation.

Dashed line: fifth-order approximation.

Dash-dot-dotted line: 15th-order approximation.

Dash-dotted line: tenth-order approximation.