Asymptotic regularity results for a viscosity version of Halpern-type iterations
Recently, Cheval and Leustean computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations generated by a nonexpansive self-mapping of a metric space assuming that it has a fixed point. In the present paper, we show that their result is valid without this assumpt...
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| Published in | Optimization Vol. 74; no. 10; pp. 2457 - 2468 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis
27.07.2025
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| Abstract | Recently, Cheval and Leustean computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations generated by a nonexpansive self-mapping of a metric space assuming that it has a fixed point. In the present paper, we show that their result is valid without this assumption. It is enough either to assume the existence of a bounded orbit of the nonexpansive mapping or the existence of a bounded sequence of approximate fixed points of the mapping. |
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| AbstractList | Recently, Cheval and Leustean computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations generated by a nonexpansive self-mapping of a metric space assuming that it has a fixed point. In the present paper, we show that their result is valid without this assumption. It is enough either to assume the existence of a bounded orbit of the nonexpansive mapping or the existence of a bounded sequence of approximate fixed points of the mapping. |
| Author | Zaslavski, Alexander J. |
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| SubjectTerms | Asymptotic regularity Halpern iteration nonexpansive mapping strict contraction |
| Title | Asymptotic regularity results for a viscosity version of Halpern-type iterations |
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