An Inverse Result of Approximation by Sampling Kantorovich Series

Abstract

In the present paper, an inverse result of approximation, i.e., a saturation theorem for the sampling Kantorovich operators is derived, in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, here we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by P.L. Butzer. At the end, some other applications of such representation formula are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs.

Inverse approximation and GBS of bivariate Kantorovich type sampling series

“…Butzer and Stens studied the saturation results for the univariate generalised sampling operators in ( [21]). Recently, the inverse results for the Kantorovich type sampling operators have been derived for the spaces C 2 (R) and C 1 (R) in ( [28]), ( [16]) respectively.…”

Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications

“…Here, we consider the above NN operators, with coefficients expressed by Kantorovich means in a multivariate form. It is well-know that this kind of approach based on Kantorovich-type operators is the most suitable in order to approximate not necessarily continuous data ( [2,11,22,33]). For this reason, we study the above operators in the general setting of Orlicz spaces, which is a very general context, which includes, as particular cases, the L p -spaces.…”

A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium

“…In the last years, the theory of sampling Kantorovich operators has been studied from different points of view, eg, in previous studies, some theoretical results have been obtained, while in Cluni et al, application in seismic engineering has been derived. In the latter case, some models have been developed for studying the behaviors of buildings under seismic action.…”