Extensions to the Jackson-type and Landau-Kolmogorov-type sharp inequalities for derivatives of low order.
The authors generalized the results obtained by \textit{V. V. Zhuk} [Approximation of periodic functions. Leningrad: Izdat. Leningr. Univ. (1982; Zbl 0521.42003)] regarding the sharp Kolmogorov-Jackson and Akhiezer-Krein-Favard-type inequalities. More exactly, for derivatives of low order the above inequalities are strengthened by passing to finer characteristics of the functions that majorize the moduli of continuity. The results are valid for best approximation by means of splines as well as for an arbitrary step of the modulus of continuity. This is the most important contribution of the authors.
scientific article; zbMATH DE number 2181919