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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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