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Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained. 相似文献
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V. S. Balaganskii 《Mathematical Notes》2006,79(3-4):299-313
We construct a convex smooth antiproximinal set in any infinite-dimensional space c 0(Γ) equipped with the Day norm; moreover, the distance function to the set is Gâteaux differentiable at each point of the complement. 相似文献
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V.S. Balaganskii 《Journal of Approximation Theory》1997,89(3):372-379
In this work we study a relative Chebyshev center ofKwith respect toY, whereKis a closed bounded convex subset of a Hilbert spaceX, andYis a closed convex subset ofX. Some results of Amir and Mach [J. Approx. Theory40, (1984), 364–374] are extended. 相似文献
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V. S. Balaganskii 《Mathematical Notes》2013,93(1-2):12-28
This paper deals with the continuity of the sharp constant K(T,X) with respect to the set T in the Jackson-Stechkin inequality $E(f,L) \leqslant K(T,X)\omega (f,T,X),$ , where E(f,L) is the best approximation of the function f ∈ X by elements of the subspace L ? X, and ω is a modulus of continuity, in the case where the space L 2( $\mathbb{T}^d $ , ?) is taken for X and the subspace of functions g ∈ L 2( $\mathbb{T}^d $ , ?), for L. In particular, it is proved that the sharp constant in the Jackson-Stechkin inequality is continuous in the case where L is the space of trigonometric polynomials of nth order and the modulus of continuity ω is the classical modulus of continuity of rth order. 相似文献
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V. S. Balaganskii 《Mathematical Notes》1996,60(5):485-494
Closed convex bounded antiproximinal bodies are constructed in the infinite-dimensional spacesC(Q), C
0(T), L(S, S, ), andB(S), whereQ is a topological space andT is a locally compact Hausdorff space. It is shown that there are no closed bounded antiproximinal sets in Banach spaces with the Radon-Nikodym property.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 643–657, November, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00196. 相似文献
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V. S. Balaganskii 《Mathematical Notes》1991,49(3):318-323
Translated from Matematicheskie Zametki, Vol. 49, No. 3, pp. 135–144, March, 1991. 相似文献
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