A study on the convergence of perturbed sampling Kantorovich operators with environmental applications

This thesis contributes to the study of perturbed sampling Kantorovich operators, by obtaining approximation results in the general context of modular spaces. We have begun by studying convergence in modular spaces through a density approach, deducing a modular convergence theorem in Orlicz spaces as a particular case. In these spaces, the rate of approximation is examined through both quantitative and qualitative estimates based on the modulus of smoothness. In addition to the theoretical contributions, this thesis also shows practical applications of the theory through a concrete case study in the field of image processing.