Proceedings of the Japan Academy, Series A, Mathematical Sciences

Self-similar measures for iterated function systems driven by weak contractions

Kazuki Okamura

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 94, Number 4 (2018), 31-35.

Dates
First available in Project Euclid: 5 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1522915216

Digital Object Identifier
doi:10.3792/pjaa.94.31

Subjects
Primary: 28A80: Fractals [See also 37Fxx] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Keywords
Self-similar measures iterated function systems weak contractions Kantorovich-Rubinstein duality theorem

Citation

Okamura, Kazuki. Self-similar measures for iterated function systems driven by weak contractions. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 4, 31--35. doi:10.3792/pjaa.94.31. https://projecteuclid.org/euclid.pja/1522915216


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