On approximation of \(2\pi \)-periodic functions in Hölder spaces
The paper is devoted to study the approximation of \(2\pi\) periodic functions belonging to generalized Hölder spaces.In the first part,some results concerning the moduli of smoothness of first and higher order are recalled. Then, a family of integral operators is introduced. Two very interesting and nice results in connection with these operators are established. The first of them contains the approximation order in terms of higher order moduli of smoothness. The second expresses the asymptotic behaviour of approximation when the approximated function belong to a generalized Hölder space. The results are applied to Vallée-Poussin operators and to Abel means.
scientific article; zbMATH DE number 2140987