Dickmeis, W.; Nessel, R. J.; van Wickeren, E. Quantitative extensions of the uniform boundedness principle. (English) Zbl 0634.41027 Jahresber. Dtsch. Math.-Ver. 89, 105-134 (1987). During the past decade the authors have developed a functional analytic approach to the problem of the sharpness of the various concrete error bounds arising in approximation theory and numerical analysis. See the monograph of the first two authors [Quantitative Prinzipien gleichmäßiger Beschränktheit und Schärfe von Fehlerabschätzungen, Forchungsber. Landes Nordrhein-Westfalen 3117, 110 S. (1982; Zbl 0493.41045)]. The purpose of this paper is to survey recent results in the subject. Reviewer: H.R.Dowson Cited in 20 Documents MSC: 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A25 Rate of convergence, degree of approximation 41-02 Research exposition (monographs, survey articles) pertaining to approximations and expansions 42A45 Multipliers in one variable harmonic analysis 42A10 Trigonometric approximation 41A55 Approximate quadratures 41A05 Interpolation in approximation theory Keywords:error bounds PDF BibTeX XML Cite \textit{W. Dickmeis} et al., Jahresber. Dtsch. Math.-Ver. 89, 105--134 (1987; Zbl 0634.41027)