Some convergence theorems for monotone nonexpansive mappings in hyperbolic metric spaces. (English) Zbl 1500.47115
Summary: In this paper, we prove strong and \(\Delta\)-convergence theorem for monotone nonexpansive mapping in a partially ordered hyperbolic metric space using Mann iteration scheme. Moreover, we give an numerical example to illustrate the main result in this paper.
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H05 | Monotone operators and generalizations |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
Keywords:
fixed point; monotone nonexpansive mapping; Mann’s iteration; hyperbolic metric spaces; strong convergenceReferences:
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