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 |
| _version_ | 1797789929902702592 |
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| author | Eduardo Daniel Jorquera Álvarez |
| author_facet | Eduardo Daniel Jorquera Álvarez |
| author_sort | Eduardo Daniel Jorquera Álvarez |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T01:57:38Z |
| format | Article |
| id | doaj.art-a1560dd9168a4d9b8119b2251ff6decf |
| institution | Directory Open Access Journal |
| issn | 2193-5343 2193-5351 |
| language | English |
| last_indexed | 2024-03-13T01:57:38Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Arabian Journal of Mathematics |
| spelling | doaj.art-a1560dd9168a4d9b8119b2251ff6decf2023-07-02T11:07:55ZengSpringerOpenArabian Journal of Mathematics2193-53432193-53512023-02-0112229730710.1007/s40065-023-00419-yOn monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert spaceEduardo Daniel Jorquera Álvarez0Departamento de Matemáticas, Universidad de La SerenaAbstract 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.https://doi.org/10.1007/s40065-023-00419-yPrimary 47H1047H05Secondary 46C0546B40 |
| spellingShingle | Eduardo Daniel Jorquera Álvarez On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space Arabian Journal of Mathematics Primary 47H10 47H05 Secondary 46C05 46B40 |
| title | On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space |
| title_full | On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space |
| title_fullStr | On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space |
| title_full_unstemmed | On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space |
| title_short | On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space |
| title_sort | on monotone pseudocontractive operators and krasnoselskij iterations in an ordered hilbert space |
| topic | Primary 47H10 47H05 Secondary 46C05 46B40 |
| url | https://doi.org/10.1007/s40065-023-00419-y |
| work_keys_str_mv | AT eduardodanieljorqueraalvarez onmonotonepseudocontractiveoperatorsandkrasnoselskijiterationsinanorderedhilbertspace |