منابع مشابه
Functionally closed sets and functionally convex sets in real Banach spaces
Let $X$ be a real normed space, then $C(subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)subseteq Bbb R $ is convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)subseteq Bbb R $ is closed for all bounded linear transformations $Tin B(X,R)$. We improve the Krein-Milman theorem ...
متن کاملContinuous Convex Sets and Zero Duality Gap for Convex Programs
This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we are able to characterize objective functions and respectively feasib...
متن کاملfunctionally closed sets and functionally convex sets in real banach spaces
let $x$ be a real normed space, then $c(subseteq x)$ is functionally convex (briefly, $f$-convex), if $t(c)subseteq bbb r $ is convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$ is functionally closed (briefly, $f$-closed), if $t(k)subseteq bbb r $ is closed for all bounded linear transformations $tin b(x,r)$. we improve the krein-milman theorem ...
متن کاملStrong proximinality of closed convex sets
We show that in a Banach space X every closed convex subset is strongly proximinal if and only if the dual norm is strongly sub differentiable and for each norm one functional f in the dual space X∗, JX(f) the set of norm one elements in X where f attains its norm is compact. As a consequence, it is observed that if the dual norm is strongly sub differentiable then every closed convex subset of...
متن کاملOn Convergence of Closed Convex Sets
In this paper we introduce a convergence concept for closed convex subsets of a finite dimensional normed vector space. This convergence is called C-convergence. It is defined by appropriate notions of upper and lower limits. We compare this convergence with the well-known Painlevé–Kuratowski convergence and with scalar convergence. In fact, we show that a sequence (An)n∈N C-converges to A if a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1971
ISSN: 0022-247X
DOI: 10.1016/0022-247x(71)90214-9