Related papers: An approximation theorem for non-decreasing functi…

We present an approximation theorem for continuous non-decreasing functions on compact preordered spaces, leading to an algebraic characterization of their corresponding function spaces. As an application, we prove that the family of…

The Stone-Weierstrass approximation theorem is extended to certain unbounded sets in $C^n$. In particular, on a locally rectifiable arc going to infinity, each continuous function can be approximated by entire functions.

The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in…

The aim of the present article is to extend the Stone--Weierstrass theorem to functions ranging in a lattice normed space and order rather than topological approximation. We proceed with the machinery of Boolean valued transfer from lattice…

In this paper we present a Stone-Weierstrass type result in the context of continuous interval-valued functions defined on a compact Hausdorff space. Namely, we provide a constructive proof of the approximation.

We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.

We give a new proof of the Kat\v{e}tov-Tong theorem. Our strategy is to first prove the theorem for compact Hausdorff spaces, and then extend it to all normal spaces. The key ingredient is how the ring of bounded continuous real-valued…

We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem of a…

An technically interesting proof of a known theorem.

In this paper we use the Vandermonde matrices and their properties to give a new proof of the classical result of Karl Weierstrass about the approximation of continuous functions $f$ on closed intervals, using a sequence of polynomials. The…

Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space and the set of representing or Jensen measures for this cone. In this paper we prove non-compact versions of this theorem.

We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…

By using a general formalism, we expose a simplified proof of the convergence of the B\'ezier polynomials attached to a continuous function defined in arbitrary dimensional simplex. We obtain an error estimate that contains the error in…

This note contains a Stone-style representation theorem for compact Hausdorff spaces.

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

We prove a variant of the Lavrentiev's approximation theorem that allows us to approximate a continuous function on a compact set K in C without interior points and with connected complement, with polynomial functions that are nonvanishing…