Convergence of the Sequence of Successive Approximations to a Fixed Point
If (X,d) is a complete metric space and T is a contraction on X, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations {Tnx} of T starting from any point x∈X converges to a unique fixed point. In this paper, using the concept...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/716971 |
| _version_ | 1828122668863324160 |
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| author | Tomonari Suzuki |
| author_facet | Tomonari Suzuki |
| author_sort | Tomonari Suzuki |
| collection | DOAJ |
| description | If (X,d) is a complete metric space and T is a contraction on X, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations {Tnx} of T starting from any point x∈X converges to a unique fixed point. In this paper, using the concept of τ-distance, we obtain simple, sufficient, and necessary conditions of the above conclusion. |
| first_indexed | 2024-04-11T14:39:37Z |
| format | Article |
| id | doaj.art-776a5dc938a14be1856c71d3bb0069e6 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-04-11T14:39:37Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-776a5dc938a14be1856c71d3bb0069e62022-12-22T04:18:02ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-01201010.1155/2010/716971Convergence of the Sequence of Successive Approximations to a Fixed PointTomonari SuzukiIf (X,d) is a complete metric space and T is a contraction on X, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations {Tnx} of T starting from any point x∈X converges to a unique fixed point. In this paper, using the concept of τ-distance, we obtain simple, sufficient, and necessary conditions of the above conclusion.http://dx.doi.org/10.1155/2010/716971 |
| spellingShingle | Tomonari Suzuki Convergence of the Sequence of Successive Approximations to a Fixed Point Fixed Point Theory and Applications |
| title | Convergence of the Sequence of Successive Approximations to a Fixed Point |
| title_full | Convergence of the Sequence of Successive Approximations to a Fixed Point |
| title_fullStr | Convergence of the Sequence of Successive Approximations to a Fixed Point |
| title_full_unstemmed | Convergence of the Sequence of Successive Approximations to a Fixed Point |
| title_short | Convergence of the Sequence of Successive Approximations to a Fixed Point |
| title_sort | convergence of the sequence of successive approximations to a fixed point |
| url | http://dx.doi.org/10.1155/2010/716971 |
| work_keys_str_mv | AT tomonarisuzuki convergenceofthesequenceofsuccessiveapproximationstoafixedpoint |