Some remarks about the convergence of composition operators

Abstract This article presents a new sequence of positive linear operators that results from recent advancements in the area of composition operators. We introduce the moment-generating function and utilize it to compute moments of certain orders. Regarding the convergence, we establish fundamental approximation theorems as well as Voronovskaya-type and Grüss-Voronovskaya-type theorems. Moreover, the difference estimates of the Baskakov-Kantorovich-type and our newly defined composition operators are also provided.