Contractive multifunctions, fixed point inclusions and iterated multifunction systems. (English) Zbl 1115.47043

The authors draw some simple consequences from the contraction mapping theorem for set-valued contractions [cf., e.g., H. Covitz and S. B. Nadler, Isr. J. Math. 8, 5–11 (1970; Zbl 0192.59802)] and give an application to an integral inclusion.


47H10 Fixed-point theorems
47H04 Set-valued operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
47N99 Miscellaneous applications of operator theory


Zbl 0192.59802
Full Text: DOI


[1] Barnsley, M.F., Fractals everywhere, (1989), Academic Press New York · Zbl 0691.58001
[2] Barnsley, M.F.; Demko, S., Iterated function systems and the global construction of fractals, Proc. roy. soc. London ser. A, 399, 243-275, (1985) · Zbl 0588.28002
[3] Barnsley, M.F.; Ervin, V.; Hardin, D.; Lancaster, J., Solution of an inverse problem for fractals and other sets, Proc. natl. acad. sci. USA, 83, 1975-1977, (1985) · Zbl 0613.28008
[4] Centore, P.; Vrscay, E.R., Continuity of fixed points for attractors and invariant measures for iterated function systems, Canad. math. bull., 37, 315-329, (1994) · Zbl 0810.58021
[5] Covitz, H.; Nadler, S.B., Multi-valued contraction mappings in generalized metric spaces, Israel J. math., 8, 5-11, (1970) · Zbl 0192.59802
[6] Fisher, Y., Fractal image compression, theory and application, (1995), Springer-Verlag New York
[7] Forte, B.; Vrscay, E.R., Theory of generalized fractal transforms, () · Zbl 0922.58046
[8] Forte, B.; Vrscay, E.R., Inverse problem methods for generalized fractal transforms, () · Zbl 0829.28005
[9] Hutchinson, J., Fractals and self-similarity, Indiana univ. J. math., 30, 713-747, (1981) · Zbl 0598.28011
[10] Kisielewicz, M., Differential inclusions and optimal control, Math. appl., (1990), Kluwer
[11] Kunze, H.; Vrscay, E.R., Solving inverse problems for ordinary differential equations using the Picard contraction mapping, Inverse problems, 15, 745-770, (1999) · Zbl 0978.34013
[12] Lu, N., Fractal imaging, (2003), Academic Press New York
[13] Vrscay, E.R.; Saupe, D., Can one break the ‘collage barrier’ in fractal image coding?, (), 307-323 · Zbl 0960.68165
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.