Sentence examples for maximal fixed point from inspiring English sources

If the conditions in Theorem 2.1 are satisfied, then has the minimal fixed point and the maximal fixed point in ; that is, and are fixed points of, and for any fixed point of in, one has.

Hence, f has a maximal fixed point.

Then the operator T has a minimal fixed point (x^) and a maximal fixed point (y^).

Since, is the minimal fixed point of and is the maximal fixed point of.

This means x ∗ is a maximal fixed point of T, and the proof is completed.

The fixed point of is said to be a maximal fixed point of if whenever and.

That means that u, ū are the minimal and maximal fixed points of Q on [v0, w0], respectively.

Next, we prove that (underline{u}(t)) and (overline{u}(t)) are the minimal and maximal fixed points of (Q_{2}) in ([v_{0},w_{0}]), respectively.

(i) If (H4) holds, then C λ has minimal and maximal fixed points in [ u 0, v 0 ] for λ ∈ ( 0, λ ∗ ].

If (H4) holds, then C λ has minimal and maximal fixed points in [ u 0, v 0 ] for λ ∈ ( 0, λ ∗ ].

Motivated by the results of [3, 8, 9], in this paper we study the existence of the minimal and maximal fixed points of a discontinuous operator, which is expressed as the form.