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Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces. (English) Zbl 0834.47048

Let \(X\) be a \(p\)-uniformly smooth Banach space, \(1\leq p\leq 2\), and \(T: X\to X\) be a Lipschitzian strongly accretive map. The authors show that the Mann and the Ishikawa iteration processes converge strongly to the unique solution of the equation \(Tx= f\). The same conclusions are also valid if \(C\subset X\) is a bounded, closed subset and \(T: C\to C\) is Lipschitzian and pseudo-contractive.

MSC:

47H06 Nonlinear accretive operators, dissipative operators, etc.
47J25 Iterative procedures involving nonlinear operators
47J05 Equations involving nonlinear operators (general)
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