Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in \(\operatorname {CAT}(0)\) spaces. (English) Zbl 1393.47027
Summary: In this paper, a new modified proximal point algorithm involving fixed point iterates of asymptotically nonexpansive mappings in \(\operatorname {CAT}(0)\) spaces is proposed and the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a common fixed point of asymptotically nonexpansive mappings is proved.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
convex minimization problem; resolvent identity; \(\operatorname{CAT}(0)\) space; proximal point algorithm; asymptotically nonexpansive mappingReferences:
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