Geodesic
Cyclical contractive mappings in hyperbolic spaces
Minimax theory and its applications, Tome 8 (2023) no. 2
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We consider a complete metric space of cyclical nonexpansive mappings acting on a union of two sets in a complete hyperbolic space. Using the porosity notion we show that most cyclical non expansive mappings are contractive. In the case when the intersection of the sets is empty we show that the distance between iterates of a contractive mapping converges to the distance between these two sets.
Mots-clés : Complete metric space, cyclical mapping, generic element, iterate, porous set 
@article{MTA_2023_8_2_a1,
     author = {Alexander J. Zaslavski},
     title = {Cyclical contractive mappings in hyperbolic spaces},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {2},
     zbl = {1527.54076},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a1/}
}
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Alexander J. Zaslavski. Cyclical contractive mappings in hyperbolic spaces. Minimax theory and its applications, Tome 8 (2023) no. 2. http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a1/