Polynomials with a parabolic majorant and the Duffin-Schaeffer inequality
Here is given a very nice result which can be looked upon as an inequality for polynomials with the parabolic majorant. This is an extension of a famous, old inequality due to Duffin and Schaeffer dealing essentially with the relation between an \(n\)th degree polynomial and the \(n\)th Chebyshev polynomial. A number of auxiliary results are quoted with proof in most cases. Bounds for relevant magnitudes are obtained. A proof of the authors' main theorem is then given and it is followed by additional contributions and remarks on their theorem.
scientific article; zbMATH DE number 89637