This brief explores the Krasnosel'ski-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

Offers a self-contained presentation of both classical and new results for interdisciplinary research Contains cutting-edge techniques and various applications Discusses recent applications of KM in large-scale optimization methods

Inhalt

1. Introduction.- 2. Notation and Mathematical Foundations.-3. The Krasnoselskii-Mann Iteration.- 4. Relations of the Krasnosel'skii-Mann Iteration and the Operator Splitting Methods.- 5. The Inertial Krasnoselskii-Mann Iteration.- 6. The Multi-step Inertial Krasnoselskii-Mann Iteration.- 7. Relaxation Parameters of the Krasnoselskii-Mann Iteration.- 8. Two Applications.