Sentence examples for maximal element and from inspiring English sources

((mathscr{P}, preceq)) has a maximal element and a minimal element.

To see the connection between the idea of a maximal element and AC, let us return to the latter's formulation AC2 in terms of indexed sets.

By the same methods as to prove Theorem 3.2, we can prove that has a maximal element and is a fixed point of in.

As an application, we derive a result on the existence of a maximal element and an almost coincidence point theorem in hyperconvex spaces.

Then, applying the extension of Zorn's lemma, the range P i ( S i, x − i ) has a maximal element; and hence T i ( x ) is a nonempty subset of S i.

The simulation of Hamiltonian [3] may realized with no greater complexity than (O( td Vert H Vert _mathrm{max} + frac{log (1/ epsilon )}{log log (1/ epsilon )})), where t is a interval of time, d is a sparse of Hamiltonian, (Vert H Vert _mathrm{max}) is a value of Hamiltonian's maximal element, and (epsilon ) stands for accuracy.

In 2006 [13], he proved a best approximation theorem and applied it to the existence of maximal elements and coincidence points.

Park [16] gave some comments on fixed points, maximal elements, and equilibria of economies in abstract convex spaces.

((F x), succeq )) is bi-inductive with a finite number of maximal elements and a finite number of minimal elements, for every (x in P).

By applying Theorem LD, Du [7] gave a generalized Brézis-Browder principle, system (vectorial) versions of Ekeland's variational principle and maximal element principle and a vectorial version of Takahashi's nonconvex minimization theorem.

In this paper, first a new form of the symmetric vector equilibrium problem is introduced and the relationship between the maximal element lemma and Ky Fan's lemma is discussed.