  The purpose of this paper is to construct a bivariate generalization of new
family of Kantorovich type sampling operators $(K_w^{\varphi}f)_{w>0}.$ First,
we give the pointwise convergence theorem and a Voronovskaja type theorem for
these Kantorovich generalized sampling series. Further, we obtain the degree of
approximation by means of modulus of continuity and quantitative version of
Voronovskaja type theorem for the family $(K_w^{\varphi}f)_{w>0}.$ Finally, we
give some examples of kernels such as box spline kernels and Bochner-Riesz
kernel to which the theory can be applied.
