Strong Converse Inequality for the Bernstein-Durrmeyer Operator Original Research Article

An equivalence relation between the rate of approximation of Bernstein-Durrmeyer polynomials and an appropriate K-functional is established. The results are stronger than those known for Bernstein polynomials. The advantages of Bernstein-Durrmeyer polynomials, i.e., self-adjointness, communativity, and simple expansion by orthogonal polynomials, are used extensively.