On Kantorovich-type Operators in Lp Spaces

This note is devoted to the study of a linear positive sequence of operators representing an integral form in Kantorovich's sense. We prove that this sequence converges to the identity operator in Lp([0,1]), p ≥ 1, spaces. By using the r-th order (r = 1 and r ≥ 3) modulus of smoothness measured in these spaces, we establish an upper bound of the approximation error. Also, we point out a connection between the smoothness of α- Hölder (0 < α ≤ 1) functions and the local approximation property.