\(L^ p\)-inverse theorems for beta operators
For the global degree of approximation of functions \(f\in L_ p[0,\infty)\), \(1\leq p\leq\infty\), by the method of Beta operators in the \(L_ p\)-metric direct and converse results are proved which can be combined to an equivalence result. The proofs make use of a large number of lemmata, a Bernstein type inequality and the equivalence of the Ditzian-Totik modulus of smoothness with an appropriate \(K\)-functional.
scientific article; zbMATH DE number 21718