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Self-similar measures for iterated function systems driven by weak contractions. (English) Zbl 1396.28018

Summary: We show the existence and uniqueness for self-similar measures for iterated function systems driven by weak contractions. Our main idea is using the duality theorem of Kantorovich-Rubinstein and equivalent conditions for weak contractions established by Jachymski. We also show collage theorems for such iterated function systems.

MSC:

28A80 Fractals
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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