Graph convergence with an application for system of variational inclusions and fixed-point problems
Abstract This paper aims at proposing an iterative algorithm for finding an element in the intersection of the solutions set of a system of variational inclusions and the fixed-points set of a total uniformly L-Lipschitzian mapping. Applying the concepts of graph convergence and the resolvent operat...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02848-3 |
| _version_ | 1811183299546054656 |
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| author | Javad Balooee Jen-Chih Yao |
| author_facet | Javad Balooee Jen-Chih Yao |
| author_sort | Javad Balooee |
| collection | DOAJ |
| description | Abstract This paper aims at proposing an iterative algorithm for finding an element in the intersection of the solutions set of a system of variational inclusions and the fixed-points set of a total uniformly L-Lipschitzian mapping. Applying the concepts of graph convergence and the resolvent operator associated with an Ĥ-accretive mapping, a new equivalence relationship between graph convergence and resolvent-operator convergence of a sequence of Ĥ-accretive mappings is established. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a common point of the above two sets is proved under some suitable hypotheses imposed on the parameters and mappings. At the same time, the notion of H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive mapping that appeared in the literature, where H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ is an α, β-generalized accretive mapping, is also investigated and analyzed. We show that the notions H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive and Ĥ-accretive operators are actually the same, and point out some comments on the results concerning them that are available in the literature. |
| first_indexed | 2024-04-11T09:45:43Z |
| format | Article |
| id | doaj.art-bfa2a53d5c3d49da90a421edfa336674 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-11T09:45:43Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-bfa2a53d5c3d49da90a421edfa3366742022-12-22T04:31:05ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-08-012022114310.1186/s13660-022-02848-3Graph convergence with an application for system of variational inclusions and fixed-point problemsJavad Balooee0Jen-Chih Yao1School of Mathematics, Statistics and Computer Science, College of Science, University of TehranResearch Center for Interneural Computing, China Medical University Hospital, China Medical UniversityAbstract This paper aims at proposing an iterative algorithm for finding an element in the intersection of the solutions set of a system of variational inclusions and the fixed-points set of a total uniformly L-Lipschitzian mapping. Applying the concepts of graph convergence and the resolvent operator associated with an Ĥ-accretive mapping, a new equivalence relationship between graph convergence and resolvent-operator convergence of a sequence of Ĥ-accretive mappings is established. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a common point of the above two sets is proved under some suitable hypotheses imposed on the parameters and mappings. At the same time, the notion of H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive mapping that appeared in the literature, where H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ is an α, β-generalized accretive mapping, is also investigated and analyzed. We show that the notions H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive and Ĥ-accretive operators are actually the same, and point out some comments on the results concerning them that are available in the literature.https://doi.org/10.1186/s13660-022-02848-3System of variational inclusionsĤ-accretive mappingTotal uniformly L-Lipschitzian mappingH ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive mappingResolvent-operator techniqueIterative algorithm |
| spellingShingle | Javad Balooee Jen-Chih Yao Graph convergence with an application for system of variational inclusions and fixed-point problems Journal of Inequalities and Applications System of variational inclusions Ĥ-accretive mapping Total uniformly L-Lipschitzian mapping H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive mapping Resolvent-operator technique Iterative algorithm |
| title | Graph convergence with an application for system of variational inclusions and fixed-point problems |
| title_full | Graph convergence with an application for system of variational inclusions and fixed-point problems |
| title_fullStr | Graph convergence with an application for system of variational inclusions and fixed-point problems |
| title_full_unstemmed | Graph convergence with an application for system of variational inclusions and fixed-point problems |
| title_short | Graph convergence with an application for system of variational inclusions and fixed-point problems |
| title_sort | graph convergence with an application for system of variational inclusions and fixed point problems |
| topic | System of variational inclusions Ĥ-accretive mapping Total uniformly L-Lipschitzian mapping H ( ⋅ , ⋅ ) $H(\cdot,\cdot)$ -accretive mapping Resolvent-operator technique Iterative algorithm |
| url | https://doi.org/10.1186/s13660-022-02848-3 |
| work_keys_str_mv | AT javadbalooee graphconvergencewithanapplicationforsystemofvariationalinclusionsandfixedpointproblems AT jenchihyao graphconvergencewithanapplicationforsystemofvariationalinclusionsandfixedpointproblems |