Strong Converse Inequalities Original Research Article

Converse inequalities are proved for a family of operators that state the equivalence of two terms of error in approximation to the revelant modulus of smoothness. Such inequalities have been proved by Z. Ditzian and K. G. Ivanov with a different method. Our emphasis is that these so-called strong converse inequalities follow from some standard estimates on the derivatives of the operators without additional work; hence we extend the Ditzian-Ivanov result to a large family of operators. The method of the paper is very close in spirit to the classical parabola technique.