Localization results for the non-truncated max-product sampling operators based on Fejér and sinc-type kernels

Abstract

Abstract. In this paper, we obtain strong localization results and local direct results in the approximation of continuous functions by the non-truncated max-product sampling operators based on Fejér and sinc (Wittaker)-type kernels. These operators present potential applications in signal theory. IntroductionThe sinc-approximation operators were first introduced and studied in [19] This idea applied, for example, to the linear Bernstein operators B n pf qpxq " ř n k"0 p n,k pxqf pk{nq, where p n,k pxq "`n k˘x k p1´xq n´k and f is positive,

Approximation Results in Orlicz Spaces for Sequences of Kantorovich Max-Product Neural Network Operators

“…Indeed, for any fixed f : b] f (x) =: c < 0, we can consider the sequences (K (M ) n (f − c, ·) + c) n∈N+ that it turns out to be convergent to f (in all the above considered senses, provided f in suitable spaces). For more details, see e.g., [18,19,25].…”

“…The max-product version of several families of linear operators has been recently studied in many papers, see e.g., [16][17][18][19].…”

An Inverse Result of Approximation by Sampling Kantorovich Series

“…The operators G w allows to reconstruct (in some sense) a given continuous signal f by a sequence of its sample values, which are of the form f (k/w), k ∈ Z, w > 0. Subsequently, such operators have been widely studied by many authors, see e.g., [4,27,40,32,41,15,16,17].…”

Pointwise and uniform approximation by multivariate neural network operators of the max-product type

“…[15,16,17]. In general, discrete linear operators are dened by nite sums or series, with respect to certain indexes.…”

“…The above procedure, allows to convert linear operators into nonlinear ones, which are able to achieve an higher order of approximation with respect to their linear counterparts, see e.g., [15,16,17].…”