Sentence examples for maximal elements and from inspiring English sources

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).

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

((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.

(ii) We say that a ∈ L is an infimum (supremum) for set D ⊂ L if cl L ( D ) has the minimal (maximal) element and a = min ( cl L ( D ) ) ( a = max ( cl L ( D ) ) ), and we write then that a = inf ( D ) ( a = sup ( D ) ); here cl L ( D ) denotes the closure of D in L.  .

We say that a ∈ L is an infimum (supremum) for set D ⊂ L if cl L ( D ) has the minimal (maximal) element and a = min ( cl L ( D ) ) ( a = max ( cl L ( D ) ) ), and we write then that a = inf ( D ) ( a = sup ( D ) ); here cl L ( D ) denotes the closure of D in L. Definition 2.4 Let L be an ordered normed space with a solid cone H.