Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type (Q1378413)

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scientific article; zbMATH DE number 1117631
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Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type
scientific article; zbMATH DE number 1117631

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    Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type (English)
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    17 March 1998
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    For the equation \(Tx= f\) with Lipschitz strongly accretive operator \(T: E\to E\) in an arbitrary Banach space \(E\) it is proved that the Ishikawa and the Mann iterative methods with errors [\textit{L.-S. Liu}, J. Math. Anal. Appl. 194, No. 1, 114-125 (1995; Zbl 0872.47031)] converge strongly to the solution. Related results are obtained for the iterative approximations of fixed points of strongly pseudocontractive operators and also for the solution of the equation \(x+ Tx= f\) with \(m\)-accretive \(T: E\to E\).
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    Lipschitz strongly accretive operator
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    Ishikawa and the Mann iterative methods with errors
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    iterative approximations of fixed points
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    strongly pseudocontractive operators
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