On A.E. Convergence of Durrmeyer-Stieltjes Polynomials Original Research Article

Let v be a finite Borel measure on [0, 1]. We introduce the notation of the Durrmeyer-Stieltjes polynomials [formula] where [formula] are the basic Bernstein polynomials. We prove that the maximal operator of the sequence (Dn) is of weak type and the sequence of polynomials (Dnv) converges a.e. on [0, 1] to the absolutely continuous part of v.