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Zbl 0999.47039
Liu, Zeqing; Kang, Shin Min
Convergence theorems for $\phi$-strongly accretive and $\phi$-hemicontractive operators. (English)
[J] J. Math. Anal. Appl. 253, No.1, 35-49 (2001). ISSN 0022-247X

The paper deals with a continuous $\varphi$-strongly accretive operator $T : X \rightarrow X$ in arbitrary real Banach space $X$. It is shown that: \par 1) the equation $Tx = f$ has a unique solution; \par 2) both Mann and Ishikawa iteration methods converge strongly to the solution (under some conditions and with error terms by Y. Xu). \par The authors consider also $\varphi$-hemicontractive operators. There is a good bibliography.
[Serghey G.Suvorov (Donetsk)]

MSC 2000:: *47H06 Accretive operators, etc. (nonlinear)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: $\phi$-strongly accretive operators; $\phi$-hemicontractive operators; Mann iteration process with errors; Ishikawa iteration process with errors; fixed points

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