Joint continuous selections of multivalued mappings with nonconvex values, and their applications

A continuous version of a theorem of Lyapunov on convexity for measures with values in a Banach space is proved, and then used to obtain two results on the existence of a common continuous selection of finitely many multivalued mappings with values in a space of Bochner-integrable functions. These results are applied to the investigation of properties of solutions of differential inclusions with $m$-accretive operators.