Construction of Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces

Abstract

Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has a fixed point. In this paper, we adapt a construction due to Moloney in order to provide a sequence that converges strongly to such a fixed point.

Keywords:

• Asymptotically nonexpansive mappings
• fixed points
• hyperbolic spaces
• uniformly convex hyperbolic spaces

Mathematics Subject Classification 2010::

• 47H09
• 47H10
• 47J25

Additional information

Funding

This work has been supported by the German Science Foundation (DFG Project KO 1737/6-1) and by a grant of the Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI – UEFISCDI, project number PN-III-P1-1.1-PD-2019-0396, within PNCDI III.