Our main purpose is to introduce the concepts of upper and lower weakly (Λ, sp)- continuous multifunctions. In particular, some characterizations multifunctions are investigated.

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Vald...