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.
Reviewer: P.S.Milojević (Newark / New Jersey)
MSC:
47H06 | Nonlinear accretive operators, dissipative operators, etc. |
47J25 | Iterative procedures involving nonlinear operators |
47J05 | Equations involving nonlinear operators (general) |