Convergence theorems for \(\phi\)-strongly accretive and \(\phi\)-hemicontractive operators (Q5927552)
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scientific article; zbMATH DE number 1579934
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence theorems for \(\phi\)-strongly accretive and \(\phi\)-hemicontractive operators |
scientific article; zbMATH DE number 1579934 |
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Convergence theorems for \(\phi\)-strongly accretive and \(\phi\)-hemicontractive operators (English)
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25 November 2002
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\(\phi\)-strongly accretive operators
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\(\phi\)-hemicontractive operators
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Mann iteration process with errors
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Ishikawa iteration process with errors
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fixed points
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The paper deals with a continuous \(\varphi\)-strongly accretive operator \(T : X \rightarrow X\) in arbitrary real Banach space \(X\). It is shown that: NEWLINENEWLINENEWLINE1) the equation \(Tx = f\) has a unique solution; NEWLINENEWLINENEWLINE2) both Mann and Ishikawa iteration methods converge strongly to the solution (under some conditions and with error terms by Y. Xu). NEWLINENEWLINENEWLINEThe authors consider also \(\varphi\)-hemicontractive operators. There is a good bibliography.
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