On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space
Abstract The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state monotone versions of Theorem 12 in [F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. M...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-02-01
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| Series: | Arabian Journal of Mathematics |
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| Online Access: | https://doi.org/10.1007/s40065-023-00419-y |
| Summary: | Abstract The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state monotone versions of Theorem 12 in [F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 2.1 in [Berinde, Vasile. Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators, Annals of West University of Timisoara-Mathematics and Computer Science, vol. 56, no. 2, 2018, pp. 13–27], as well as, several related results. Further results, in Hilbert spaces without a partial order, are stated too. |
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| ISSN: | 2193-5343 2193-5351 |