We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.
Iterated function systems on functions of bounded variation / D. La Torre, F. Mendivil, E.R. Vrscay. - In: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY. - ISSN 0218-348X. - 24:2(2016), pp. 1650019.1-1650019.7.
Iterated function systems on functions of bounded variation
D. La TorrePrimo
;
2016
Abstract
We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.
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