Saturation and inverse results for the Bernstein max-product operator
The nonlinear Bernstein max-product approximation operators were defined and formally studied in [\textit{S. G. Gal}, Shape-preserving approximation by real and complex polynomials. Basel: Birkhäuser (2008; Zbl 1154.41002)]. Several articles were devoted to their study and to some related max-product type operators. As explained in the introduction of this paper, for large classes of functions, the Bernstein max-product operators improve the order of approximation to the Jackson-type order. For these operators, the authors determine the saturation order and its associated special class of functions. A local inverse result is also obtained.
scientific article; zbMATH DE number 6384182