Geodesic
Periodic Trajectories and Coincidence Points of Tuples of Set-Valued Maps
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 72-77

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A fixed-point theorem is proved for a finite composition of set-valued Lipschitz maps such that the product of their Lipschitz constants is less than 1. The notion of a Lipschitz tuple of (finitely many) set-valued maps is introduced; it is proved that such a tuple has a periodic trajectory, which determines a fixed point of the given composition of set-valued Lipschitz maps. This result is applied to study the coincidence points of a pair of tuples (Lipschitz and covering).
Keywords: set-valued map, Hausdorff metric, Lipschitz set-valued map, fixed point, surjective operator. 
@article{FAA_2018_52_2_a5,
     author = {B. D. Gel'man},
     title = {Periodic {Trajectories} and {Coincidence} {Points} of {Tuples} of {Set-Valued} {Maps}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {72--77},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a5/}
}
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B. D. Gel'man. Periodic Trajectories and Coincidence Points of Tuples of Set-Valued Maps. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 72-77. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a5/