Balázs–Shepard Operators on Infinite Intervals, II Original Research Article

The weighted uniform convergence of the Balázs–Shepard operator is considered on the real line. As a consequence of the main result, it is proved that for a wide class of weights, rational functions are always dense in the space of continuous functions, in contrast to the polynomials where the Akhiezer–Babenko condition is necessary for such density.