Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces
Let be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contrac...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/369412 |
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| author | Jong Soo Jung |
| author_facet | Jong Soo Jung |
| author_sort | Jong Soo Jung |
| collection | DOAJ |
| description | Let be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contraction defined by has a fixed point . Let , and be three sequences in satisfying approximate conditions. Then, for arbitrary , the sequence generated by
for all
converges strongly to a fixed point of . |
| format | Article |
| id | doaj-art-d14e3f6265fb420fb272793733127507 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d14e3f6265fb420fb2727937331275072025-02-03T01:02:00ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/369412369412Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach SpacesJong Soo Jung0Department of Mathematics, Dong-A University, Busan 604-714, Republic of KoreaLet be a reflexive Banach space having a weakly sequentially continuous duality mapping with gauge function , a nonempty closed convex subset of , and a multivalued nonself-mapping such that is nonexpansive, where . Let be a contraction with constant . Suppose that, for each and , the contraction defined by has a fixed point . Let , and be three sequences in satisfying approximate conditions. Then, for arbitrary , the sequence generated by for all converges strongly to a fixed point of .http://dx.doi.org/10.1155/2013/369412 |
| spellingShingle | Jong Soo Jung Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces |
| title_full | Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces |
| title_fullStr | Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces |
| title_full_unstemmed | Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces |
| title_short | Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces |
| title_sort | convergence of a viscosity iterative method for multivalued nonself mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2013/369412 |
| work_keys_str_mv | AT jongsoojung convergenceofaviscosityiterativemethodformultivaluednonselfmappingsinbanachspaces |