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Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption. (English) Zbl 0896.47048
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 $Tx= f$, $f\in E$.

##### MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H06 Accretive operators, dissipative operators, etc. (nonlinear)
##### Keywords:
strongly accretive map; Ishikawa iterative sequence
Full Text:
##### References:
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