Shape preserving approximation properties to family of α-Bernstein shifted knot operators

The main idea of this paper is to obtain approximation results by utilizing the shifted knots properties of the family of α -Bernstein operators. We examine some basic results and estimate the moments of this new family of α -Bernstein operators. We derive an upper bound on the error estimation using the usual modulus of continuity in continuous function spaces. Furthermore, we have also obtained the shape-preserving properties and discussed some direct theorems.