Strong inequalities for the iterated Boolean sums of Bernstein operators

Abstract

In this paper we investigate   the approximation properties for the iterated Boolean sums of Bernstein operators.
 The approximation behaviour of those operators is presented by the so-called strong inequalities.  Moreover, such strong inequalities
are valid for any individual continuous  function on $[0, 1]$. The obtained estimate covers global direct, inverse and   saturation results.