Study of Sensitivity of Parameters of Bernstein–Stancu Operators
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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.
KeywordsBernstein operators Bernstein–Stancu operators
Mathematics Subject Classification41A10 41A36
The authors are thankful to Rodin Lusan and Barbara Strazzabosco of Zentralblatt MATH, Berlin, Germany, who took all the trouble to manage us the paper (Stancu 1969) from Studia UBB, Romania. The authors are thankful to the reviewers for making valuable suggestions leading to a better presentation of the paper.