  In the present article, we analyse the behaviour of a new family of
Kantorovich type sampling operators $(K_w^{\varphi}f)_{w>0}.$ 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 $C({\mathbb{R}})$
(the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$)
for the family $(K_w^{\varphi}f)_{w>0}.$ Finally, we give some examples of
kernels such as B-spline kernels and Blackman-Harris kernel to which the theory
can be applied.
