Study of Sensitivity of Parameters of Bernstein–Stancu Operators

This paper is aimed at studying sensitivity of parameters \(\alpha \) and \(\beta \) appearing in the operators introduced by Stancu (Studia Universitatis Babes-Bolyai 14(2):31–45, 1969). Results are established on the behavior of 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 \(\alpha \) and \(\beta \) in Bernstein–Stancu polynomials can be used to get better approximation at a point \(x = \alpha /\beta \) in [0, 1] to the Bernstein polynomials.