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The cluster set of a nonexpansive mapping

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In questo articolo vengono esaminate alcune proprietà dell’insiameS di tutti i punti limite delle varie successionix, q (x), q 2(x), … doveq: R d →R d è una funzione nonespandibile (|q(x)−q(y)|≤|x−y|). Vengono quindi caratterizzate quelle particolari funzioni nonespandibili isometriche a tratti aventi la proprietà che per ognix, esistek (finito) per il qualeq k(x)∈S.

Sunto

Fur a nonexpansive mappingq: R d→R d, we examine some properties of the setS of all possible limit points of sequences of the formx, q (x), q 2 (x), … We then characterize those piecewise isometric nonexpansive mappings having the property: for everyx there exists a finitek such thatq k (x)∈S.

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  1. Jonathan E. Spingarn

    Present address: School of Mathematics, del Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

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    1. Jonathan E. Spingarn
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    This work was supported, in part, by the National Science Foundation, under grant # DMS-8506712.

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    Spingarn, J.E. The cluster set of a nonexpansive mapping. Seminario Mat. e. Fis. di Milano 57, 287–291 (1987). https://doi.org/10.1007/BF02925056

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