The solution by iteration of nonlinear equations in uniformly smooth Banach spaces
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.
strong convergence of the Mann and Ishikawa iterative processes
iterative solution of operator equations
scientific article; zbMATH DE number 1115444
scientific article