Aproximation properties of λ-Bernstein-Kantorovich-Stancu operators

Abstract

The goal of this paper is to construct a new type of Bernstein operators depending on the shape parameter λϵ[-1,1]. For these new type operators a uniform convergence result is presented. Furthermore, order of approximation in the sense of local approximation is investigated  and Voronovskaja type theorem is proved. Lastly, some graphical results are given to show the rate of convergence of constructed operators to a given function f.