The behavior of fixed point free nonexpansive mappings in geodesic spaces. (English) Zbl 1386.54021
Summary: Dropping the existence of fixed points of a nonexpansive mapping is an interesting and unusual task in metric fixed point theory. Hyperbolic geometry proved to be very relevant in the study of the behavior of fixed point free nonexpansive mappings. In this work, we generalize some of the results in that direction in geodesic spaces. More precisely, we show under which additional assumptions the Picard iterative sequence of a mapping defined on a hyperbolic geodesic space tends to a point of the boundary.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
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