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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 involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
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References:

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