Sharp Constants of Approximation Theory. IV. Asymptotic Relations in General Settings

DOI10.1007/S10476-022-0185-ZarXiv2002.10512MaRDI QIDQ6335484

Publication date: 24 February 2020

Abstract: In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements, and approximation on classes of elements. Second, we find sufficient conditions that imply limit relations between various sharp constants of approximation theory in general settings. Third, a number of examples from various areas of approximation theory illustrates the general approach.

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Best constants in approximation theory (41A44)

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