ON BERNSTEIN POLYNOMIALS OF FUNCTIONS OF BOUNDED VARIATION OF ORDER p

1.IntroductionLet f be a function defined on0,1],then the Bernstein poly-nomial B_n(f,x)of f is T.Popoviciu(see1])and G.G.Lorentz studied the operator(1.1)and estimated the rate of convergence of B_n(f,x).F.Herzogand J.D. Hill,and others studied the convergence of(1.1)fordiscontinuous functions,they proved that if f is bounded on0,1]and x is a discontinuity point of the first kind,then