Favard interpolation from subsets of a rectangular lattice

More on Favard interpolation from subsets of a rectangular lattice

representation theorems of $L-$subsets and $L-$families on complete residuated lattice

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

Lagrange Interpolation on a Lattice: Bounding Derivatives by Divided Differences

Fix an integer n > 0. For a multivariate function defined on a (not necessarily rectangular) lattice, an extension is constructed to have, ∀k ≤ n, derivatives of total degree k that are bounded by the function’s tensor product divided differences of total degree k times a constant independent of the lattice and the function. The extension is locally constructed, can have any prescribed smoothne...

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...

Interpolation by polynomial functions of distributive lattices : a generalization of a theorem of R. L. Goodstein

We consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein’s theorem solves a particular instance of this interpolation problem on a distributive lattice L with least and greatest elements 0 and 1, resp.: Given a function f : {0, 1}n → L, there exists a lattice polynomial function p : Ln → L such that p|{...