Sentence examples for maximal element with from inspiring English sources

For the sequel we are interested in computing the maximal element, with respect to the p-majorization order, of the set (S_{a}).

Komiya [10] showed that the Kakutani fixed point theorem can be derived from the existence theorem of maximal elements with the aid of Theorem 2.2.

Some authors also assume that the parts of a possible world w form a join semi-lattice with maximal element w (Bach 1986; Lasersohn 1988, 1990; Portner 1992; see also the entry mereology).

Every non-empty collection of terms U can be uniquely split into disjoint sets U i, such that every U i has a single maximal element (an element comparable with and not smaller than any other member) and contains all members of U comparable with its maximal element.

If a function f ∈ C+(Sn- 1) (denoted the set of positive continuous functions on Sn- 1and endowed with the topology derived from the max norm), the set { K ∈ K 0 n : h K ≤ f }. has a unique maximal element, then the Aleksandrov body associated with the function f is denoted by K ( f ) = max { K ∈ K 0 n : h K ≤ f }. (2.11).

In [7] (see also [3]), Lin and Du established the following abstract maximal element principle in a -bounded quasiordered set with a sizing-up function.

Broadly speaking, these propositions assert that certain conditions are sufficient to ensure that a partially ordered set contains at least one maximal element, that is, an element such that, with respect to the given partial ordering, no element strictly exceeds it.

F ( x ) is inductive with a finite number of maximal element clusters, for every x ∈ P. A2″.

F ( x ) is inductive with a finite number of maximal element clusters for every x ∈ P, then F has an order-clustered fixed point.

Later, the famous Brézis-Browder's maximal element principle [5] was established and applied to deal with nonlinear problems.

Yang et al. [13] proved some maximal element theorems for set-valued maps in abstract convex spaces with applications.