A characterization of the rate of approximation of Kantorovich sampling operators in variable exponent Lebesgue spaces

We establish a direct and a matching two-term converse estimate by a K -functional and a modulus of smoothness for the rate of approximation by generalized Kantorovich sampling operators in variable exponent Lebesgue spaces. They yield the saturation property and class of these operators. We also prove a Voronovskaya-type estimate.