On closed sets with convex projections under narrow sets of directions
نویسندگان
چکیده
منابع مشابه
Convex sets with homothetic projections
Nonempty sets X1 and X2 in the Euclidean space R n are called homothetic provided X1 = z+λX2 for a suitable point z ∈ R n and a scalar λ 6= 0, not necessarily positive. Extending results of Süss and Hadwiger (proved by them for the case of convex bodies and positive λ), we show that compact (respectively, closed) convex sets K1 and K2 in R n are homothetic provided for any given integer m, 2 ≤ ...
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 کاملConsecutive projections onto convex sets.
In this note we describe and evaluate the performance of a novel approach to information recovery that involves consecutive projection onto convex sets (POCS). The method is applied to a time series of medical image data and the results are compared to images reconstructed using the standard POCS reconstruction method. The consecutive POCS method converges in a desired step-wise manner producin...
متن کاملProjections onto convex sets on the sphere
In this paper some concepts of convex analysis are extended in an intrinsic way from the Euclidean space to the sphere. In particular, relations between convex sets in the sphere and pointed convex cones are presented. Several characterizations of the usual projection onto a Euclidean convex set are extended to the sphere and an extension of Moreau’s theorem for projection onto a pointed convex...
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: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04466-8