Geodesic
Cascade Search for Preimages and Coincidences: Global and Local Versions
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 127-143.

Voir la notice de l'article provenant de la source Math-Net.Ru

In previous papers of the author, the cascade search principle was proposed, which makes it possible to construct a set-valued self-map of a metric space $X$ from a set-valued functional or a collection of set-valued maps of $X$ so that the new map generates a multicascade, i.e., a set-valued discrete dynamical system whose limit set coincides with the zero set of the given functional, with the coincidence set of the given collection, or with the common preimage of a closed subspace under the maps from this collection. Stability issues of cascade search were studied. This paper is devoted to a generalization and local modifications of the cascade search principle and their applications to problems concerning local search and approximation of common preimages of subspaces and coincidence sets for finite collections of set-valued maps of metric spaces.
Keywords: cascade search, set-valued map, coincidence set, fixed point, common roots.
Mots-clés : multicascade 
@article{MZM_2013_93_1_a12,
     author = {T. N. Fomenko},
     title = {Cascade {Search} for {Preimages} and {Coincidences:} {Global} and {Local} {Versions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {127--143},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a12/}
}
TY  - JOUR
AU  - T. N. Fomenko
TI  - Cascade Search for Preimages and Coincidences: Global and Local Versions
JO  - Matematičeskie zametki
PY  - 2013
SP  - 127
EP  - 143
VL  - 93
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a12/
LA  - ru
ID  - MZM_2013_93_1_a12
ER  - 
%0 Journal Article
%A T. N. Fomenko
%T Cascade Search for Preimages and Coincidences: Global and Local Versions
%J Matematičeskie zametki
%D 2013
%P 127-143
%V 93
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a12/
%G ru
%F MZM_2013_93_1_a12
T. N. Fomenko. Cascade Search for Preimages and Coincidences: Global and Local Versions. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 127-143. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a12/

[1] T. N. Fomenko, “O priblizhenii k tochkam sovpadeniya i obschim nepodvizhnym tochkam nabora otobrazhenii metricheskikh prostranstv”, Matem. zametki, 86:1 (2009), 110–125 | DOI | MR | Zbl

[2] T. N. Fomenko, “K zadache kaskadnogo poiska mnozhestva sovpadenii nabora mnogoznachnykh otobrazhenii”, Matem. zametki, 86:2 (2009), 304–309 | DOI | MR | Zbl

[3] T. N. Fomenko, “Cascade search principle and its applications to the coincidence problem of $n$ one-valued or multi-valued mappings”, Topology Appl., 157:4 (2010), 760–773 | DOI | MR | Zbl

[4] T. N. Fomenko, “O priblizhenii k tochkam sovpadeniya konechnogo nabora otobrazhenii metricheskikh prostranstv”, Abstracts of the Fifth International Conference of Differential and Functional Differential Equations (DFDE-2008) (Moscow, Russia, August 17–24, 2008), 119

[5] T. N. Fomenko, “Printsip kaskadnogo poiska i sovpadeniya $N$ otobrazhenii”, Materialy mezhdunarodnoi konferentsii “Covremennye problemy matematiki, mekhaniki i ikh prilozhenii”, posvyaschennoi 70-letiyu V. A. Sadovnichego (30 marta–02 aprelya 2009 g., MGU, Moskva), 99

[6] A. V. Arutyunov, “Nakryvayuschie otobrazheniya v metricheskikh prostranstvakh i nepodvizhnye tochki”, DAN, 416:2 (2007), 151–155 | MR | Zbl

[7] A. V. Arutyunov, “Ustoichivost tochek sovpadeniya i svoistva nakryvayuschikh otobrazhenii”, Matem. zametki, 86:2 (2009), 163–169 | DOI | MR | Zbl

[8] T. N. Fomenko, “The stability of Cascade Search Principle”, Abstracts of the 2010 International Conference on Topology and its Applications (June 26–30, Nafpaktos, Greece), Nafpaktos, 2010, 99

[9] T. N. Fomenko, “Ustoichivost kaskadnogo poiska”, Izv. RAN. Ser. matem., 74:5 (2010), 171–190 | DOI | MR | Zbl

[10] T. N. Fomenko, “Kaskadnyi poisk: ustoichivost dostizhimykh predelnykh tochek”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2010, no. 5, 3–9 | MR

[11] T. N. Fomenko, “New developments in the cascade search theory”, Abstracts of the 8-th International ISAAC Congress (Moscow, August 22–27), 2011, 369

[12] A. Arutyunov, E. Avakov, B. Gel'man,A. Dmitruk, V. Obukhovskii, “Locally covering maps in metric spaces and coincidence points”, J. Fixed Point Theory Appl., 2009, no. 5, 105–127 | DOI | MR | Zbl