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Zbl 0896.47048
Zhou, Haiyun
Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption.
(English)
[J] J. Math. Anal. Appl. 213, No.1, 296-307 (1997). ISSN 0022-247X

Let $E$ be a real Banach space with a uniformly convex dual space $E^*$. Suppose $T: E\to E$ is a continuous (not necessarily Lipschitzian) strongly accretive map such that $(I- T)$ has bounded range, where $I$ denotes the identity operator. It is proved that the Ishikawa iterative sequence converges strongly to the unique solution of the equation $Tx= f$, $f\in E$.
[J.Appell (Würzburg)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H06 Accretive operators, etc. (nonlinear)

Keywords: strongly accretive map; Ishikawa iterative sequence

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