Cascade Search: Stability of Reachable Limit Points / Fomenko T.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. ? 5. P. 3-9 [Moscow Univ. Math. Bulletin. Vol. 65, No 5, 2010. P. 179-185].

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.

Key words: cascade search stability, multivalued mappings, subspace preimage, coincidence of n mappings.