Proof.By Korovkin-type theorem

1 Introduction One of the cornerstone theorems in approximation theory is the Weierstrass approximation [ 1 ] theorem, which proves that any continuous function defined on a closed interval can be uniformly approximated by polynomials. In 1912, Bernstein [ 2 ] introduced the Bernstein operators to provide a constructive proof of the Weierstrass theorem. Bernstein operators have become a classical tool in approximation theory.