Simultaneous approximation for combinations of Szász-Durrmeyer operators (Q1887398)

The authors consider linear combinations of Szász-Durrmeyer operators and prove an equivalence result for simultaneous approximation, in terms of a weighted modulus of smoothness \(\omega^{2r}_{\varepsilon^\lambda}\), with \(0\leq\lambda\leq 1\) and \(\varphi(x)= \sqrt{x}\). The use of this modulus is very elegant, since it provides at the same time a global and a local estimate; moreover, it bridges the gap between the classical modulus (obtained for \(\lambda= 0\)) and the Ditzian-Totik modulus \((\lambda= 1)\).