Improving certain Bernstein-type approximation processes

This paper deals with a modification of the classical Bernstein polynomials defined on the unit simplex. It introduces a new sequence of non-polynomial linear operators which hold fixed the polynomials x2+αx and y2+βy with α,β∈[0,+∞). We study the convergence properties of the new approximation process and certain shape properties that are preserved. Finally, we compare it with Bernstein polynomials and show an improvement of the error of convergence in certain subsets of the simplex.