Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings
We study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach space E which has a Fréchet differentiable norm or its dual E* has the Kadec-Klee property. Moreover, weak convergence of projection type...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/745451 |
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| author | Tanakit Thianwan |
| author_facet | Tanakit Thianwan |
| author_sort | Tanakit Thianwan |
| collection | DOAJ |
| description | We study weak convergence of the projection type Ishikawa iteration scheme
for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach
space E which has a Fréchet differentiable norm or its dual E* has the Kadec-Klee property. Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically
nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréchet differentiable norm is proved. Some results have been obtained which generalize and unify many important known results in recent literature. |
| format | Article |
| id | doaj-art-eeffaf8e71d14be5adf8383762ee1a38 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-eeffaf8e71d14be5adf8383762ee1a382025-02-03T01:04:18ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/745451745451Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-MappingsTanakit Thianwan0School of Science, University of Phayao, Phayao 56000, ThailandWe study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach space E which has a Fréchet differentiable norm or its dual E* has the Kadec-Klee property. Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréchet differentiable norm is proved. Some results have been obtained which generalize and unify many important known results in recent literature.http://dx.doi.org/10.1155/2011/745451 |
| spellingShingle | Tanakit Thianwan Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings Abstract and Applied Analysis |
| title | Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings |
| title_full | Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings |
| title_fullStr | Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings |
| title_full_unstemmed | Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings |
| title_short | Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings |
| title_sort | weak convergence of the projection type ishikawa iteration scheme for two asymptotically nonexpansive nonself mappings |
| url | http://dx.doi.org/10.1155/2011/745451 |
| work_keys_str_mv | AT tanakitthianwan weakconvergenceoftheprojectiontypeishikawaiterationschemefortwoasymptoticallynonexpansivenonselfmappings |