Fractal Polynomials and Maps in Approximation of Continuous Functions. (2nd January 2016)

• Record Type: Journal Article
• Authors: Viswanathan, P.; Navascués, M. A.; Chand, A. K. B.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 1(2016)
• Page Start: 106
• Page End: 127
• Publication Date: 2016-01-02
• Subjects: Best approximation -- constrained approximation -- fractal interpolation function -- fractal polynomial -- SAIN property; 28A80 -- 41A29 -- 41A30 -- 41A50 -- 58C05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1078816
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The primary goal of this article is to establish some approximation properties of fractal functions. More specifically, we establish that a monotone continuous real-valued function can be uniformly approximated with a monotone fractal polynomial, which in addition agrees with the function on an arbitrarily given finite set of points. Furthermore, the simultaneous approximation and \mboxinterpolation which is norm-preserving property of fractal polynomials is established. In the final part of the article, we establish differentiability of a more general class of fractal functions. It is shown that these smooth fractal functions and their derivatives are good approximants for the original function and its \mboxderivatives.