Geodesic
Cascade Search of the Coincidence Set of Collections of Multivalued Mappings
Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 304-309.

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The present paper is a continuation of the previous papers of the author dealing with this subject. We study the cascade search of a given subset $A$, i.e., the construction on the metric space $X$ of a multicascade with given limit subset $A$ in $X$. A multicascade is a multivalued dynamical system with translation semigroup equal to the additive semigroup of nonnegative integers. We propose a finer (than in the author's previous papers) version of cascade search for cases in which (1) $A$ is the complete preimage of a closed subspace under the multivalued mapping of metric spaces; (2) $A$ is the set of coincidence points $n$, $n>1$, of the multivalued mappings. An estimate of the distance from the initial to any corresponding limit point is given. In particular, in case (2), a new generalization of a recent theorem due to Arutyunov is obtained for $n=2$.
Keywords: multivalued mapping, cascade search, metric space, coincidence point, discrete dynamical system, translation semigroup.
Mots-clés : multicascade 
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T. N. Fomenko. Cascade Search of the Coincidence Set of Collections of Multivalued Mappings. Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 304-309. http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a12/

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[2] T. N. Fomenko, “Cascade search principle and its applications to the coincidence problem of n one-valued or multi-valued mappings”, Topology Appl. (to appear)

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