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Constructive approximation of continuous interval-valued functions

Juan Jose Font, Sergio Macario

TL;DR

A Stone-Weierstrass type result in the context of continuous interval-valued functions defined on a compact Hausdorff space is presented and a Jackson type approximation result involving the modulus of continuity of intervals based on the gH-difference of intervals is provided.

Abstract

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.

Constructive approximation of continuous interval-valued functions

TL;DR

A Stone-Weierstrass type result in the context of continuous interval-valued functions defined on a compact Hausdorff space is presented and a Jackson type approximation result involving the modulus of continuity of intervals based on the gH-difference of intervals is provided.

Abstract

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.
Paper Structure (6 sections, 14 theorems, 65 equations)

This paper contains 6 sections, 14 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. A version of the Stone-Weierstrass theorem in Interval Valued Analysis.
  4. A Jackson type approximation result for interval-valued functions.
  5. Approximation by means of interval-valued neural networks
  6. Conclusion

Key Result

Proposition 2.1

The metric $d_H$ satisfies the following properties:

Theorems & Definitions (27)

  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Definition 3.1
  • Proposition 3.2
  • proof
  • Lemma 3.3
  • Lemma 3.4
  • Proposition 3.5
  • ...and 17 more