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

May 15, January 30, February 26, Abstract. In this paper, we establish quantitative estimates for the nonlinear sampling Kantorovich operators in the general setting of modular spaces L rho. To achieve this, we consider a notion of modulus of smoothness based on the convex modular functional rho, which defines the space. The approach proposed is new in the sense that, in the literature, theorems for the order of approximation in L rho 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 L rho. To show the effectiveness of the achieved results, several particular cases of modular spaces are presented in detail.