A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings
Abstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of CAT...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02618-7 |
| _version_ | 1818608644580704256 |
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| author | Sabiya Khatoon Watcharaporn Cholamjiak Izhar Uddin |
| author_facet | Sabiya Khatoon Watcharaporn Cholamjiak Izhar Uddin |
| author_sort | Sabiya Khatoon |
| collection | DOAJ |
| description | Abstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of CAT ( 0 ) $\operatorname{CAT}(0)$ spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration. |
| first_indexed | 2024-12-16T14:45:55Z |
| format | Article |
| id | doaj.art-9744301d493b44aea9bc726530e25814 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-16T14:45:55Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-9744301d493b44aea9bc726530e258142022-12-21T22:27:47ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-04-012021112010.1186/s13660-021-02618-7A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappingsSabiya Khatoon0Watcharaporn Cholamjiak1Izhar Uddin2Department of Mathematics, Jamia Millia IslamiaSchool of Science, University of PhayaoDepartment of Mathematics, Jamia Millia IslamiaAbstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of CAT ( 0 ) $\operatorname{CAT}(0)$ spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration.https://doi.org/10.1186/s13660-021-02618-7CAT ( 0 ) $\operatorname{CAT}(0)$ spaceNearly asymptotically quasi-nonexpansive mappingsΔ-convergence |
| spellingShingle | Sabiya Khatoon Watcharaporn Cholamjiak Izhar Uddin A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings Journal of Inequalities and Applications CAT ( 0 ) $\operatorname{CAT}(0)$ space Nearly asymptotically quasi-nonexpansive mappings Δ-convergence |
| title | A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings |
| title_full | A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings |
| title_fullStr | A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings |
| title_full_unstemmed | A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings |
| title_short | A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings |
| title_sort | modified proximal point algorithm involving nearly asymptotically quasi nonexpansive mappings |
| topic | CAT ( 0 ) $\operatorname{CAT}(0)$ space Nearly asymptotically quasi-nonexpansive mappings Δ-convergence |
| url | https://doi.org/10.1186/s13660-021-02618-7 |
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