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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Autores principales:	Yuanheng Wang, Xiuping Wu, Chanjuan Pan
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2020
Materias:	Split common fixed point Strong convergence Variational inequality Asymptotically nonexpansive mapping Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/af4d0215eb8d4bb1900cf3ecd7987f95
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spelling	oai:doaj.org-article:af4d0215eb8d4bb1900cf3ecd7987f952021-12-02T15:11:21ZThe iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces10.1186/s13663-020-00686-w1687-1812https://doaj.org/article/af4d0215eb8d4bb1900cf3ecd7987f952020-12-01T00:00:00Zhttps://doi.org/10.1186/s13663-020-00686-whttps://doaj.org/toc/1687-1812Abstract 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.Yuanheng WangXiuping WuChanjuan PanSpringerOpenarticleSplit common fixed pointStrong convergenceVariational inequalityAsymptotically nonexpansive mappingApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2020, Iss 1, Pp 1-12 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Split common fixed point Strong convergence Variational inequality Asymptotically nonexpansive mapping Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Split common fixed point Strong convergence Variational inequality Asymptotically nonexpansive mapping Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Yuanheng Wang Xiuping Wu Chanjuan Pan The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces
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.
format	article
author	Yuanheng Wang Xiuping Wu Chanjuan Pan
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
publishDate	2020
url	https://doaj.org/article/af4d0215eb8d4bb1900cf3ecd7987f95
work_keys_str_mv	AT yuanhengwang theiterativesolutionsofsplitcommonfixedpointproblemforasymptoticallynonexpansivemappingsinbanachspaces AT xiupingwu theiterativesolutionsofsplitcommonfixedpointproblemforasymptoticallynonexpansivemappingsinbanachspaces AT chanjuanpan theiterativesolutionsofsplitcommonfixedpointproblemforasymptoticallynonexpansivemappingsinbanachspaces AT yuanhengwang iterativesolutionsofsplitcommonfixedpointproblemforasymptoticallynonexpansivemappingsinbanachspaces AT xiupingwu iterativesolutionsofsplitcommonfixedpointproblemforasymptoticallynonexpansivemappingsinbanachspaces AT chanjuanpan iterativesolutionsofsplitcommonfixedpointproblemforasymptoticallynonexpansivemappingsinbanachspaces
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The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

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