Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces
Let X be a real uniformly smooth Banach space and let T:D(T)⫅X→X be a K-positive definite operator. Under suitable conditions we establish that the iterative method by Bai (1999) converges strongly to the unique solution of the equation Tx=f, f∈X. The results presented in this paper generalize the...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005919 |
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| _version_ | 1832558101142700032 |
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| author | Zeqing Liu Shin Min Kang Jeong Sheok Ume |
| author_facet | Zeqing Liu Shin Min Kang Jeong Sheok Ume |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| description | Let X be a real uniformly smooth Banach space and let
T:D(T)⫅X→X be a
K-positive definite
operator. Under suitable conditions we establish that the
iterative method by Bai (1999) converges strongly to the unique
solution of the equation Tx=f, f∈X. The results presented
in this paper generalize the corresponding results of Bai (1999),
Chidume and Aneke (1993), and Chidume and Osilike (1997). |
| format | Article |
| id | doaj-art-5ff888a9cb0141fe9cd0d11cbe0dae6b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5ff888a9cb0141fe9cd0d11cbe0dae6b2025-02-03T01:33:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127315516010.1155/S0161171201005919Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spacesZeqing Liu0Shin Min Kang1Jeong Sheok Ume2Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaDepartment of Mathematics, Gyeongsang National University, Chinju 660-701, KoreaDepartment of Applied Mathematics, Ghangwon National University, Changwon 641-773, KoreaLet X be a real uniformly smooth Banach space and let T:D(T)⫅X→X be a K-positive definite operator. Under suitable conditions we establish that the iterative method by Bai (1999) converges strongly to the unique solution of the equation Tx=f, f∈X. The results presented in this paper generalize the corresponding results of Bai (1999), Chidume and Aneke (1993), and Chidume and Osilike (1997).http://dx.doi.org/10.1155/S0161171201005919 |
| spellingShingle | Zeqing Liu Shin Min Kang Jeong Sheok Ume Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces |
| title_full | Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces |
| title_fullStr | Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces |
| title_full_unstemmed | Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces |
| title_short | Iterative solutions of K-positive definite operator equations in real uniformly smooth Banach spaces |
| title_sort | iterative solutions of k positive definite operator equations in real uniformly smooth banach spaces |
| url | http://dx.doi.org/10.1155/S0161171201005919 |
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