Inequalities for a class of \({\mathcal {B}}_n\)-operators

Bernstein-type inequalities play a very important role in the theory of approximation. During last few decades, a number of operators have been identified, which preserve such type of inequalities between polynomials. In this paper, we consider a more general operator belonging to the family \({\mathcal {B}}_n\) ${\mathcal{B}}_n$ and establish some inequalities preserved by it, which generalize or refine some of the results proved earlier.