Approximation by Max-Product Sampling Operators Based on Sinc-Type Kernels

Approximation by max-product type nonlinear operators

The purpose of this survey is to present some approximation and shape preserving properties of the so-called nonlinear (more exactly sublinear) and positive, max-product operators, constructed by starting from any discrete linear approximation operators, obtained in a series of recent papers jointly written with B. Bede and L. Coroianu. We will present the main results for the max-product opera...

Max-Product Shepard Approximation Operators

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp...

On approximation properties of sampling operators defined by dilated kernels

In this paper we consider some generalized Shannon sampling operators, which are defined by band-limited kernels. In particular, we use dilated versions of some previously known kernels. We give also some examples of using sampling operators with dilated kernels in imaging applications.

Statistical σ approximation to max-product operators

On Approximation of Functions by Product Operators

In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α, r), 1 ≤ r < ∞ and the weighted class W (Lr, ξ(t)), 1 ≤ r < ∞ by (C, 2)(E, 1) product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.