Variation on Butzerʹs problem: Characterization of the solutions

The so-called Butzer problem had been a challenge to the approximation community for decades until its first constructive solution was given by Cao and Gonska at the end of the 1980s. Butzerʹs original problem can be turned into a “strong form”, namely a pointwise one. In the present note, we characterize, among other things, and in an easy way, certain operators which solve Butzerʹs problem in this strong and most demanding version.