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 Grüss-Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given.