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math.FA2018
Extensions of Bernstein's Lethargy Theorem
Asuman Güven Aksoy
In this paper, we examine the aptly-named "Lethargy Theorem" of Bernstein and survey its recent extensions. We show that one of these extensions shrinks the interval for best appro…
math.FA2018
Bernstein Lethargy Theorem and Reflexivity
Asuman Güven Aksoy, Qidi Peng
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let be an arbitrary…