Quantitative translations for viscosity approximation methods in hyperbolic spaces. (English) Zbl 1495.47106
The authors show, in a very general metric framework, that convergence of what they call ‘Browder-type sequences’ (i.e., approximating curves of resolvents) and of Halpern iterations imply the convergence of the corresponding viscosity algorithms. They also derive, using proof mining techniques, rates of metastability for the viscosity algorithms conditional on rates of metastability for the corresponding Browder/Halpern sequences. In addition, in the case where the target point of the iteration is unique, they derive convergence rates by using the modulus of uniqueness technique.
Reviewer: Andrei Sipoş (Bucureşti)
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 03F10 | Functionals in proof theory |
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
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