Study of sensitivity of parameters of Bernstein-Stancu operators

Abstract

This paper is aimed at studying sensitivity of parameters αand βappearing 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 αand βin Bernstein-Stancu polynomials can be used to get better approximation at a point x = (α)/(β) in [0,1] to the Bernstein polynomials.