An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem
The multiple-sets split equality problem (MSSEP) requires finding a point x∈∩i=1NCi, y∈∩j=1MQj such that Ax=By, where N and M are positive integers, {C1,C2,…,CN} and {Q1,Q2,…,QM} are closed convex subsets of Hilbert spaces H1, H2, respectively, and A:H1→H3,...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/620813 |
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| _version_ | 1849387163006795776 |
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| author | Luoyi Shi Ru Dong Chen Yu Jing Wu |
| author_facet | Luoyi Shi Ru Dong Chen Yu Jing Wu |
| author_sort | Luoyi Shi |
| collection | DOAJ |
| description | The multiple-sets split equality problem (MSSEP) requires finding a point x∈∩i=1NCi, y∈∩j=1MQj such that Ax=By, where N and M are positive integers, {C1,C2,…,CN} and {Q1,Q2,…,QM} are closed convex subsets of Hilbert spaces H1,
H2, respectively, and A:H1→H3,
B:H2→H3 are two bounded linear operators. When N=M=1, the MSSEP is called the split equality problem (SEP). If B=I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient. |
| format | Article |
| id | doaj-art-331309d847a147ddae069cc94829ca2c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-331309d847a147ddae069cc94829ca2c2025-08-20T03:55:22ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/620813620813An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality ProblemLuoyi Shi0Ru Dong Chen1Yu Jing Wu2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaTianjin Vocational Institute, Tianjin 300410, ChinaThe multiple-sets split equality problem (MSSEP) requires finding a point x∈∩i=1NCi, y∈∩j=1MQj such that Ax=By, where N and M are positive integers, {C1,C2,…,CN} and {Q1,Q2,…,QM} are closed convex subsets of Hilbert spaces H1, H2, respectively, and A:H1→H3, B:H2→H3 are two bounded linear operators. When N=M=1, the MSSEP is called the split equality problem (SEP). If B=I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.http://dx.doi.org/10.1155/2014/620813 |
| spellingShingle | Luoyi Shi Ru Dong Chen Yu Jing Wu An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem Abstract and Applied Analysis |
| title | An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem |
| title_full | An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem |
| title_fullStr | An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem |
| title_full_unstemmed | An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem |
| title_short | An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem |
| title_sort | iterative algorithm for the split equality and multiple sets split equality problem |
| url | http://dx.doi.org/10.1155/2014/620813 |
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