Abstract
The concept of strict approximation over subspaces of an euclidean space, introduced by John R. Rice, is extended to closed convex sets. It is proved that the best p-approximants converge as p→∞ to the strict approximant not generally but when the closed convex set satisfies certain approximative property. Finally, a similar problem is considered in the space c0 of real sequences tending to 0.
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References
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This paper was partially supported by the Consojo de Investigacions Cient/ficas y Tecnológicas de la Provincia de Córdoba.
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Marano, M. Strict approximation on closed convex sets. Approx. Theory & its Appl. 6, 99–109 (1990). https://doi.org/10.1007/BF02836199
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DOI: https://doi.org/10.1007/BF02836199