Local iterations for nonlinear systems involving uniformly accretive operators in arbitrary normed linear spaces (Q1598348)

This article deals with Mann and Ishikawa iterations for an inclusion \(f\in Ax\) with a uniformly continuous and uniformly accretive multivalued map \(A: D(A)\subset E\to 2^E\) with open domain \(D(A)\) under the assumption that this inclusion has a solution \(x^*\in D(A)\), where \(E\) is an arbitrary real normed linear space. The main result is a theorem about the strong convergence of Mann and Ishikawa iterations to \(x^*\). As applications, similar results for an inclusion \(x\in Tx+ f\) with uniformly continuous and uniformly pseudocontractive map \(T: D(T)\subset E\to 2^E\) with an open \(D(T)\) are proved. Also, Mann and Ishikawa iteration processes with errors are studied. A comprehensive comparison of these results with known ones is presented.