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The solution by iteration of nonlinear equations in uniformly smooth Banach spaces. (English) Zbl 0906.47050
Let \(E\) be a uniformly smooth Banach space and let \(T:D(T)\subseteq E\to E\) be a strong pseudocontraction with an open domain \(D(t)\) in \(E\) and a fixed point \(x^*\in D(T)\). The authors establish the strong convergence of the Mann and Ishikawa iterative processes (with errors) to the fixed point of \(T\). Related results deal with the iterative solution of operator equations of the form \(f\in Tx\) and \(f\in x+\lambda Tx\), \(\lambda>0\), when \(T\) is a set-valued strongly accretive operator. The theorems include the cases in which the operator \(T\) is defined only locally. Explicit error estimates are also given.
Reviewer: U.Kosel (Freiberg)

MSC:
47J25 Iterative procedures involving nonlinear operators
47H04 Set-valued operators
47J05 Equations involving nonlinear operators (general)
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