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April 2018 Self-similar measures for iterated function systems driven by weak contractions
Kazuki Okamura
Proc. Japan Acad. Ser. A Math. Sci. 94(4): 31-35 (April 2018). DOI: 10.3792/pjaa.94.31

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.

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Kazuki Okamura. "Self-similar measures for iterated function systems driven by weak contractions." Proc. Japan Acad. Ser. A Math. Sci. 94 (4) 31 - 35, April 2018. https://doi.org/10.3792/pjaa.94.31

Information

Published: April 2018
First available in Project Euclid: 5 April 2018

zbMATH: 06929331
MathSciNet: MR3783543
Digital Object Identifier: 10.3792/pjaa.94.31

Subjects:
Primary: 28A80 , 47H09

Keywords: iterated function systems , Kantorovich-Rubinstein duality theorem , self-similar measures , weak contractions

Rights: Copyright © 2018 The Japan Academy

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Vol.94 • No. 4 • April 2018
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