Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping. (English) Zbl 1477.47083
Summary: In this paper, we prove strong convergence and \(\varDelta\)-convergence of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping (i.e., nearly asymptotically nonexpansive mapping) in partially ordered hyperbolic metric space. Moreover, we prove stability of Fibonacci-Mann iteration. Further, we construct a numerical example to illustrate results. Our results simultaneously generalize the results of M. R. Alfuraidan and M. A. Khamsi [Bull. Aust. Math. Soc. 96, No. 2, 307–316 (2017; Zbl 06792047)] and J. Schu [J. Math. Anal. Appl. 158, No. 2, 407–413 (1991; Zbl 0734.47036)].
MSC:
| 47J26 | Fixed-point iterations |
| 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:
hyperbolic metric space; nearly asymptotically nonexpansive mapping; Fibonacci-Mann iteration; monotone non-Lipschitzian mapping; fixed point theorems; strong convergence; \(\varDelta\)-convergence; stabilityReferences:
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