共查询到20条相似文献,搜索用时 15 毫秒
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G. E. Ivanov 《Mathematical Notes》2010,87(3-4):355-366
We consider the existence and uniqueness of the farthest point of a given set A in a Banach space E from a given point x in the space E. It is assumed that A is a convex, closed, and bounded set in a uniformly convex Banach space E with Fréchet differentiable norm. It is shown that, for any point x sufficiently far from the set A, the point of the set A which is farthest from x exists, is unique, and depends continuously on the point x if and only if the set A in the Minkowski sum with some other set yields a ball. Moreover, the farthest (from x) point of the set A also depends continuously on the set A in the sense of the Hausdorff metric. If the norm ball of the space E is a generating set, these conditions on the set A are equivalent to its strong convexity. 相似文献
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Farthest points of sets in uniformly convex banach spaces 总被引:4,自引:0,他引:4
Michael Edelstein 《Israel Journal of Mathematics》1966,4(3):171-176
LetS be a closed and bounded set in a uniformly convex Banach spaceX. It is shown that the set of all points inX which have a farthest point inS is dense. Letb(S) denote the set of all farthest points ofS, then a sufficient condition for
to hold is thatX have the following property (I): Every closed and bounded convex set is the intersection of a family of closed balls. 相似文献
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Y. Chiang 《Journal of Global Optimization》2010,46(3):465-473
In this paper, we derive an existence result for generalized variational inequalities associated with multivalued mappings
on weakly compact sets under a continuity assumption which is much weaker than the regular complete continuity. As an application,
we prove the existence of exceptional families of elements for such mappings on closed convex cones in reflexive Banach spaces
when the corresponding complementarity problems have no solutions. 相似文献
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We give an example of a weakly compact set in a Banach space, which does not embed topologically as a weakly compact subset
of Hilbert space. We also show that a weakly compact set embeds in a super-reflexive space iff it embeds in Hilbert space.
This work was done while the authors were visiting Ohio State University. We wish to thank the Department of mathematics at
Ohio State University for their kind hospitality.
The work of the first author was partially supported by NSF Grant MPS-74-24249.
The work of the second author is a part of his Ph.D. Thesis prepared at the University of California at Berkeley. 相似文献
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G. R. Wood 《Israel Journal of Mathematics》1986,54(3):351-365
By associating with an affine dependence the resultant of a related probability measure, we are able to define the set ofdivisible points, D(K), of a compact convex setK. Some general properties ofD(K) are discussed, and its equivalence with a set recently introduced by Reay for convex polytopes demonstrated. For polytopes,D(K) is a continuous image of a projective space. A conjecture concerningD(K) is settled affirmatively for cubes. 相似文献
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E. M. Bronshtein 《Siberian Mathematical Journal》1995,36(1):17-23
The research was financially supported by the Russian Foundation for Fundamental Research (Grant 94-01-01286). 相似文献
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Tudor Zamfirescu 《Mathematische Zeitschrift》1997,226(4):623-630
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Vassilis Kanellopoulos 《Israel Journal of Mathematics》2000,117(1):61-69
A sufficient condition for a Banach spaceX is given so that every weakly compact Chebyshev subset ofX is convex. For this purpose a class broader than that of smooth Banach spaces is defined. In this way a former result of A. Brøndsted and A. L. Brown is partially extended in every finite dimensional normed linear space and a known result in Hilbert spaces is proved in a different way. 相似文献
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Antonio Avilés 《Israel Journal of Mathematics》2007,159(1):189-204
We consider the cardinal invariant CG(X) of the minimal number of weakly compact subsets which generate a Banach space X. We study the behavior of this index when passing to subspaces, its relation with the Lindelöf number in the weak topology and other related questions. 相似文献
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Ioana Ghenciu 《Monatshefte für Mathematik》2020,191(4):719-733
In this paper we introduce p-Dunford–Pettis completely continuous operators and study Banach spaces with the wp-Dunford–Pettis relative compact property (wp-DPrcP). We study the behaviour of p-Dunford–Pettis completely operators on spaces with this property. We give sufficient conditions for spaces of operators to have the wp-DPrcP. 相似文献
17.
Edgar Asplund 《Israel Journal of Mathematics》1966,4(4):213-216
IfS is a bounded and closed subset of a Banach spaceB, which is both reflexive and locally uniformly rotund, then, except on a set of first Baire category, the points inB have farthest points inS. 相似文献
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The main result is that every weakly compact operator between Banach spaces factors through a reflexive Banach space. Applications of the result and technique of proof include new results (e.g., separable conjugate spaces embed isomorphically in spaces with boundedly complete bases; convex weakly compact sets are affinely homeomorphic to sets in a reflexive space) and simple proofs of known results (e.g., there is a reflexive space failing the Banach-Saks property; if X is separable, then for some Z; there is a separable space which does not contain l1 whose dual is nonseparable). 相似文献