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.
References in periodicals archive ?
Let p [greater than or equal to] 2 be fixed, X be a real Banach space and K a non-empty, convex subset of X.
Let K be a nonempty, closed and convex subset in H.
n] : X (x) [greater than or equal to] [alpha]} is a nonempty compact, convex subset of [R.
Let C be a nonempty convex subset of a real Banach space E with dual E*.
Let K be a nonempty closed convex subset of X and T : K [right arrow] K be a mapping.
1]) Assume that C is a closed convex subset of a real Hilbert space H.
Since the closure B = cl(S(a)) is a closed, idempotent, bounded and absolutely convex subset in A (see, for example, [27], pp.
3] Let E be a real Banach space, K be a nonempty closed convex subset of E, [T.
For all x [member of] ir(dom(f)), [partial derivative]f (x) is a non-empty closed convex subset.
n] :X(x) [greater than or equal to] [alpha]} is a non empty compact convex subset of [R.