Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping
In this paper, we prove strong convergence and Δ−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 const...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-09-01
|
| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2019-0030 |
| Summary: | In this paper, we prove strong convergence and Δ−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 Alfuraidan and Khamsi [Bull. Aust. Math. Soc., 2017, 96, 307–316] and Schu [J. Math. Anal. Appl., 1991, 58, 407–413]. |
|---|---|
| ISSN: | 2391-4661 |