Estimations for the convex modular of the aliasing error of nonlinear sampling Kantorovich operators

In this paper, we establish quantitative estimates for the nonlinear sampling Kantorovich operators in the general setting of modular spaces Lρ. To achieve this, we consider a notion of modulus of smoothness based on the convex modular functional ρ, which defines the space. The approach proposed is new in the sense that, in the literature, theorems for the order of approximation in Lρ are mainly qualitative, i.e., are proved considering functions belonging to Lipschitz classes; here the estimates are achieved for every function belonging to the whole Lρ. To show the effectiveness of the achieved results, several particular cases of modular spaces are presented in detail.