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Minimax Theory and its Applications 08 (2023), No. 2, 285--300
Copyright Heldermann Verlag 2023

Cyclical Contractive Mappings in Hyperbolic Spaces

Alexander J. Zaslavski
Dept. of Mathematics, Technion -- Israel Institute of Technology, Haifa, Israel

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 nonexpansive 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.

Keywords: Complete metric space, cyclical mapping, generic element, iterate, porous set.

MSC: 47H09, 47H10, 54E50, 54E52.

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