Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces
By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3645 |
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| _version_ | 1832561940891697152 |
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| author | Yali Zhao Zunquan Xia Zeqing Liu |
| author_facet | Yali Zhao Zunquan Xia Zeqing Liu |
| author_sort | Yali Zhao |
| collection | DOAJ |
| description | By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solutions of the generalized set-valued variational-like inclusions and the convergence criteria of the two iterative algorithms for the generalized set-valued variational-like inclusions in reflexive Banach spaces. The results presented in this paper are new and are an extension of the corresponding results in this direction. |
| format | Article |
| id | doaj-art-dc0ba3f392b1412b9de2e14d0faa2072 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dc0ba3f392b1412b9de2e14d0faa20722025-02-03T01:23:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005223645365910.1155/IJMMS.2005.3645Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spacesYali Zhao0Zunquan Xia1Zeqing Liu2Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, ChinaDepartment of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, ChinaDepartment of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, ChinaBy using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solutions of the generalized set-valued variational-like inclusions and the convergence criteria of the two iterative algorithms for the generalized set-valued variational-like inclusions in reflexive Banach spaces. The results presented in this paper are new and are an extension of the corresponding results in this direction.http://dx.doi.org/10.1155/IJMMS.2005.3645 |
| spellingShingle | Yali Zhao Zunquan Xia Zeqing Liu Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces |
| title_full | Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces |
| title_fullStr | Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces |
| title_full_unstemmed | Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces |
| title_short | Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces |
| title_sort | generalized set valued variational like inclusions and wiener hopf equations in banach spaces |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3645 |
| work_keys_str_mv | AT yalizhao generalizedsetvaluedvariationallikeinclusionsandwienerhopfequationsinbanachspaces AT zunquanxia generalizedsetvaluedvariationallikeinclusionsandwienerhopfequationsinbanachspaces AT zeqingliu generalizedsetvaluedvariationallikeinclusionsandwienerhopfequationsinbanachspaces |