Construction of graph-directed invariant sets of weak contractions on semi-metric spaces
Metric Geometry
2026-03-30 v2 Classical Analysis and ODEs
Functional Analysis
Abstract
We present a construction of graph-directed invariant sets of weak contractions in the sense of Matkowski-Rus on semi-metric spaces. We follow the approach by Bessenyei and P\'enzes, which applies the Kuratowski noncompactness measure without relying on Blascke's completeness theorem. We also establish a relationship between this approach and a generalized de Rham's functional equation indexed by a finite directed graph.
Keywords
Cite
@article{arxiv.2503.23423,
title = {Construction of graph-directed invariant sets of weak contractions on semi-metric spaces},
author = {Kazuki Okamura},
journal= {arXiv preprint arXiv:2503.23423},
year = {2026}
}
Comments
v2: minor revision; 21 pages, 4 figures; to appear in Aequationes Mathematicae