Approximation by Hermite-type sampling operators in Lp-norms

Recently, the so-called Hermite-type sampling operators have been introduced as extensions of the well-known generalized sampling operators for the approximation of differentiable functions. By integrating derivative values of the target function into their formulation, Hermite-type sampling operators provide several advantages, including a higher order of approximation, a reduced number of sampling points, and sharper error estimates. In this paper, we improve some results previously obtained and we address the problem of approximating the function (and its derivatives) in Lp-spaces by means of averaged moduli of smoothness. As a consequence, we extend convergence results in Lp-spaces for generalized sampling operators to the case of kernels that are not necessarily compactly supported.