Approximation of infinite dimensional fractals generated by integral equations
type: Item
instance of: scholarly article
title: Approximation of infinite dimensional fractals generated by integral equations
zbMATH Open document ID: 1203.28005
author: B. E. Eshmatov
published in: Journal of Computational and Applied Mathematics
publication date: 2010-05-21T00:00:00Z
review text: The authors present an interesting research result: For a Fredholm integral equation \[ u(x)= f(x)+\lambda \int^b_a K(x, y)u(y)\,dy,\quad f\in C([a,b]), \quad K\in C([a,b]\times[a,b]), \] consider \(K^i:[a,b]\times[a,b]\to\mathbb{R}\) and \(f^i:[a,b]\to \mathbb{R}\), \(1\leq i\leq h\). Then define contractions \(T^i: u\to v^i\) by \[ T^i(u):= v^i(x)= f^i(x)+\lambda \int^b_a K^i(x,y) u(y)\,dy. \] Let \(\{T^i: 1\leq i\leq h\}\) be an iterated function system, and \[ F(B)= \bigcup^h_{i=1} T^i(B). \] Then the attractor \(A\) generated by this IFS, has the property \(H(A,A_n)\to 0\), where \(H\) is the Hausdorff metric of \(A\) and \(A_n\).
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 5710747
zbMATH Keywords: attractor
zbMATH Keywords: fractal
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: iterated function system (IFS)
zbMATH Keywords: orthogonal projection
reviewed by: Su Weiyi
MaRDI profile type: Publication
full work available at URL: j.cam.2010.02.017
OpenAlex ID: W2019240708
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DOI: 10.1016/J.CAM.2010.02.017
description: scientific article; zbMATH DE number 5710747