Approximation by certain linear operators preserving $x^2$

Abstract

We investigate certain positive linear operators $L_n$ preserving the functions $e_k(x) = x^k , k = 0, 1$, and modified operators $L^∗_n$ which preserve $e_0$ and $e_2$ . We show that the error of approximation of f by $L^∗_n(f)$ is smaller than for $L_n(f)$.