A converse theorem on weighted approximation of functions with singularities by Bernstein operators

Let f be functions with singularities at endpoints, and the smooth modulus. The present paper discuss the weighted approximation to functions with singularities and get the converse theorem as follows: w|B_n* (f, x) - f(x)| = O[[φ^1-λ(x)/√n]^s] → ω²_φ^λ (f, t)_w = O(t^s)´ which generalize the result of Vecchia-Mastroianni-Totik in [2].