On stability of iteration processes convergent to stationary points of semigroups of nonlinear operators in metric spaces
Wojciech M. Kozƚowski · Optimization · 2024
Let C be a closed subset of a complete metric space. In this paper we study the stability problem for some iteration processes that approximate stationary points of pointwise Lipschitzian semigroups of nonlinear mappings acting within C. We show that a large class of well-controlled processes is stable under summable errors. These results are then applied to the stability of some known processes including the generalized Krasnosel'skii-Mann and the two-step Ishikawa iteration processes.