Stability of iteration processes weakly convergent to stationary points of semigroups of nonlinear operators
摘要
Let C be a bounded, closed, convex subset of a Banach space. We investigate stability of iteration processes approximating stationary points of pointwise Lipschitzian semigroups of nonlinear mappings acting within C. We show that the well-controlled processes are stable under summable errors, and then apply this result to the Krasnosel’skii–Mann and the two-step Ishikawa iteration processes.