Tan, Kok-Keong; Xu, Hong-Kun Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces. (English) Zbl 0834.47048 J. Math. Anal. Appl. 178, No. 1, 9-21 (1993). 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) Cited in 3 ReviewsCited in 52 Documents MSC: 47H06 Nonlinear accretive operators, dissipative operators, etc. 47J25 Iterative procedures involving nonlinear operators 47J05 Equations involving nonlinear operators (general) Keywords:\(p\)-uniformly smooth Banach space; Lipschitzian strongly accretive map; Mann and the Ishikawa iteration processes; Lipschitzian; pseudo- contractive PDFBibTeX XMLCite \textit{K.-K. Tan} and \textit{H.-K. Xu}, J. Math. Anal. Appl. 178, No. 1, 9--21 (1993; Zbl 0834.47048) Full Text: DOI