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V. S. Balaganskii 《Mathematical Notes》1977,22(3):681-687
A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace
inl
p
(1<p≠2). A metric projection onto a boundedly compact set inl
p
is sequentially weakly upper semicontinueus. An example is given on a convex, compact set inl
2 onto which the metric projection is not weakly continuous.
Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 345–356, September, 1977. 相似文献
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V. S. Balaganskii 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):48-62
We consider an abstract attainability problem with constraints of asymptotic nature defined in the form of a nonempty family of subsets in the space of ordinary solutions. Various variants of implementing asymptotic effects are considered (convergence in a topological space, cycles, and so on). A rather general method is suggested for presenting the results of action of approximate solutions; this method generalizes constructions based on sequences in the space of ordinary solutions. 相似文献
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V. S. Balaganskii 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):78-102
In the space L
2 of real-valued measurable 2π-periodic functions that are square summable on the period [0, 2π], the Jackson-Stechkin inequality
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$
E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2
$
E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2
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