Constructive Approximation of Continuous Interval-Valued Functions. (25th January 2022)

• Record Type: Journal Article
• Authors: Font, Juan J.; Macario, Sergio
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 2(2022)
• Page Start: 127
• Page End: 144
• Publication Date: 2022-01-25
• Subjects: Interval neural networks -- interval-valued continuous functions -- Jackson-type theorem -- Stone-Weierstrass theorem; 41A30 -- 65G40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2007949
• Languages: English
• ISSNs: 0163-0563

Abstract

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. We also provide a Jackson type approximation result involving the modulus of continuity of interval-valued functions based on the gH -difference of intervals. Finally we show how an interval-valued continuous function can be approximated using interval neural networks. All the proofs are constructive.