On stability of fixed points of multivalued maps (Q5946921)

Generalizing result of \textit{B. O'Neill} [Am. J. Math. 75, 497-509 (1953; Zbl 0050.39202)] and \textit{G. Gabor} [Math. Japan. 40, No. 2, 361-369 (1994; Zbl 0812.54047)], the authors give criteria for the stability of an isolated fixed point of a convex-valued multivalued map in a Banach space w.r.t. small perturbations. These criteria are formulated for compact and condensing maps in terms of the topological index.