Iterative process for an \(\alpha\)-nonexpansive mapping and a mapping satisfying condition (C) in a convex metric space. (English) Zbl 1455.47027
Summary: We construct one-step iterative process for an \(\alpha\)-nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study \(\triangle\)-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and valid in hyperbolic spaces, \(CAT(0)\) spaces, Banach spaces and Hilbert spaces, simultaneously.
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
convex metric space; \(\alpha\)-nonexpansive mapping; condition (C); common fixed point; one-step iterative process; convergenceReferences:
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