convex set

(redirected from Convex subset)

convex set

[′kän‚veks ′set]
(mathematics)
A set which contains the entire line segment joining any pair of its points.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Suppose K is the [sigma]-closed convex subset of M generated by {[T.sub.u](0): u [member of] [A.sup.u]}; since
where K is the discrete version of the closed convex subset K, denoted by the same symbol.
Let E be the set of fuzzy numbers and let [delta] [member of] E be a fuzzy number if and only if [[[delta]].sup.[alpha]] is a nonempty compact convex subset of [R.sup.1].
where f is a nonlinear operator defined on a convex subset D of a complex dimension space C.
Let C be a nonempty closed convex subset of a real Hilbert space H.
The fixed point set of a quasinonexpansive mapping defined on a convex subset of a strictly convex space is convex.
For two random mappings S, T: [OMEGA] x Y [right arrow] E with T([omega], Y) [subset or equal to] S([omega], Y) and C being a nonempty closed convex subset of a separable Banach space E, there exists a real number [delta] [member of] [0, 1) and a monotone increasing function [phi]: [R.sup.+] [right arrow] [R.sup.+] with [phi](0) = 0, and for all x, y [member of] C, one has
We observe that Y is compact and convex subset of the space [W.sup.1,1.sub.loc] with the topology [[tau].sup.F.sub.loc].
Further, Kirk [1] presented that each nonexpansive (single-valued) mapping on a bounded closed convex subset of a complete CAT(0) space always has a fixed point.
It follows from the well known Michael's selection Theorem [8, 9] that if the metric projection onto a closed, convex subset of a Banach space is lower semi continuous then it has a continuous selection.
Hence, let K [subset] [R.sup.n] be a compact, convex subset of [R.sup.n] and [phi]: R x K x [R.sup.n] [??] [R.sup.n] be a compact acyclic map which satisfies condition (6.1).