Asymptotic properties of powers of linear positive operators which preserve e2

AbstractIn this paper we prove Korovkin type theorem for iterates of general positive linear operators T:C[0,1]→C[0,1] which preserve e2 and derive quantitative estimates in terms of moduli of smoothness. The results can be applied to several well-known operators; we present here the Bernstein, the q-Bernstein, the genuine Bernstein–Durrmeyer and the genuine q-Bernstein–Durrmeyer operators