In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators (Kwφf)w>0. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in C(ℝ), the set of all uniformly continuous and bounded functions on ℝ for the family (Kwφf)w>0. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.

Keywords: sampling Kantorovich operators, Voronovskaya type formula, rate of convergence, modulus of smoothness.