The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces
Abstract In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved,...
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SpringerOpen
2020-12-01
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| Series: | Fixed Point Theory and Applications |
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| Online Access: | https://doi.org/10.1186/s13663-020-00686-w |
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doaj-af4d0215eb8d4bb1900cf3ecd7987f952020-12-13T12:18:51ZengSpringerOpenFixed Point Theory and Applications1687-18122020-12-012020111210.1186/s13663-020-00686-wThe iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spacesYuanheng Wang0Xiuping Wu1Chanjuan Pan2Department of Mathematics, Zhejiang Normal UniversityDepartment of Mathematics, Zhejiang Normal UniversityDepartment of Mathematics, Zhejiang Normal UniversityAbstract In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.https://doi.org/10.1186/s13663-020-00686-wSplit common fixed pointStrong convergenceVariational inequalityAsymptotically nonexpansive mapping |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yuanheng Wang Xiuping Wu Chanjuan Pan |
| spellingShingle |
Yuanheng Wang Xiuping Wu Chanjuan Pan The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces Fixed Point Theory and Applications Split common fixed point Strong convergence Variational inequality Asymptotically nonexpansive mapping |
| author_facet |
Yuanheng Wang Xiuping Wu Chanjuan Pan |
| author_sort |
Yuanheng Wang |
| title |
The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces |
| title_short |
The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces |
| title_full |
The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces |
| title_fullStr |
The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces |
| title_full_unstemmed |
The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces |
| title_sort |
iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in banach spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1812 |
| publishDate |
2020-12-01 |
| description |
Abstract In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors. |
| topic |
Split common fixed point Strong convergence Variational inequality Asymptotically nonexpansive mapping |
| url |
https://doi.org/10.1186/s13663-020-00686-w |
| work_keys_str_mv |
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