Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1071-1083 |
| Number of pages | 13 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 445 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2017 |
Keywords
- Geodesic boundary
- Geodesic spaces
- Nonexpansive mappings
- Picard iterative sequence
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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