Approximation properties of λ -Kantorovich operators

In the present paper, we study a new type of Bernstein operators depending on the parameter \(\lambda\in[-1,1]\). The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Gruss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given.