Perturbations compactes des contractions multivoques. (Compact perturbations of multivalued contractions) (Q810917)

The problem of existence of fixed points for multifunctions of the form \(\psi =f+\phi,\) where \(\phi\) is a multivalued contraction on a Banach space and f is a single-valued perturbation, is investigated. The author proves that \(\psi\) has fixed points if \(\phi\) has closed convex values and f is continuous with conditionally compact range. Some other results and counterexamples are also given.