Generalized \(\alpha\)-nonexpansive mappings in hyperbolic spaces. (English) Zbl 07589358
Summary: This paper deals with the new iterative algorithm for approximating the fixed point of generalized \(\alpha\)-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized \(\alpha\)-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.
MSC:
| 47A06 | Linear relations (multivalued linear operators) |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
| 49M05 | Numerical methods based on necessary conditions |
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