Inverse Theorems for Bernstein Polynomials

The lower estimate for linear positive operators, I

“…In many cases such investigations lead to so-called inverse or saturation results. For the first type of theorems the method introduced by Berens and Lorentz [1] turns out to be a simple and efficient tool. However, for the second case a different technique should be used.…”

Approximation by rational operators in Lp spaces

“…By the well-known result of Berens and Lorentz [2], we have finished (1.4). Finally, (1.5) can be deduced by the same way as [5] or [10].…”

Local Smoothness of Functions and Baskakov–Durrmeyer Operators

“…In fact, it was proved in [9] with a constant M f independent of n and x, if and only if | 1 ( f, t)=0(t a ), where Such an equivalence was first given by Berens and Lorentz [1] for Bernstein operators in 1972. Some more characterizations of second orders and higher orders of global smoothness of functions along this line can be found in [6,8] and [10,11] respectively.…”