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Okamura, Kazuki

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

Proc. Japan Acad., Ser. A 94, No. 4, 31-35 (2018).
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.

Cited in 3 Documents

MSC:

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

Keywords:

self-similar measures; iterated function systems; weak contractions; Kantorovich-Rubinstein duality theorem
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\textit{K. Okamura}, Proc. Japan Acad., Ser. A 94, No. 4, 31--35 (2018; Zbl 1396.28018)
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