Study of sensitivity of parameters of Bernstein-Stancu operators

This paper is aimed at studying sensitivity of parameters α and β appearing in the operators introduced by D.D. Stancu [11] in 1969. Results are established on the behavior the nodes used in Bernstein-Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein-Stancu operators and an upper bound estimation are derived. It is also established that the parameters α and β in Bernstein-Stancu polynomials can be used to get better approximation at a point x = α/β in [0, 1] to the Bernstein polynomials.