Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives
The author has treated in detail some problems of approximations in the context of optimization. The paper is an elaboration of certain results announced earlier in 1983. Main contributions are summarised in the first section through three interesting theorems. Auxiliary conclusions are given then following by proofs of theorems. Optimal quadrature formulae are constructed which help in completing the necessary arguments. This rather long paper shows several valuable aspects of extremal problems in the modern approximation theory.
scientific article; zbMATH DE number 4063739