Cascade search: Stability of reachable limit points

This paper is a continuation of the series of author’s previous works focused on the cascade search method. The stability of the subset of limit points of a given searching multi-cascade reachable from x is considered with respect to a small variation of the initial point x and to a small perturbation of the searching functional φ generating the multi-cascade. The results are applied to the cascade search problem for common preimages of a closed subspace under n (n ≥ 1) multi-valued mappings.