On the geometry and fixed point free mappings in hyperbolic spaces

DOI10.1007/S11784-018-0581-YOpenAlexW2805541104MaRDI QIDQ1615289

Bozena Piatek

Publication date: 30 October 2018

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-018-0581-y

zbMATH Keywords

visual boundaryGromov product\(\mathrm{CAT}(\kappa )\) spacefixed point free mapping

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Geodesics in global differential geometry (53C22) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Cites Work

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• The behavior of fixed point free nonexpansive mappings in geodesic spaces
• Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
• Iterating holomorphic self-mappings of the Hilbert ball
• Elements of asymptotic geometry
• The fixed point property and unbounded sets in spaces of negative curvature
• Conformal structure on the boundary and geodesic flow of a \(\text{CAT}(-1)\)-space
• Convex geodesic bicombings and hyperbolicity
• Fixed point theorems in CAT(0) spaces and \(\mathbb R\)-trees
• Fixed Point Theory in Distance Spaces
• Nonexpansive iterations in hyperbolic spaces
• Iterates of Holomorphic Self-Maps of the Unit Ball in Hilbert Space
• The boundary of a Busemann space
• A selection theorem in metric trees
• Metric spaces, convexity and nonpositive curvature

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