The circle as an attractor of an iterated function system on the plane

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Demir B., Dzhafarov V., Kocak S., Ureyen M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.332, no.1, pp.735-740, 2007 (SCI-Expanded, Scopus)

• Publication Type: Article / Article
• Volume: 332 Issue: 1
• Publication Date: 2007
• Doi Number: 10.1016/j.jmaa.2006.10.067
• Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.735-740
• Keywords: iterated function system, self-similarity
• Anadolu University Affiliated: Yes

Abstract

We give an iterated function system (IFS) on the plane with the circle as attractor. In doing this, we also give a sufficient condition for radially contracting functions on the plane (or on R-n) to be a contraction. A counterexample shows that radial contractiveness is not enough to be a contraction. (C) 2006 Elsevier Inc. All rights reserved.