Translations of quasimonotone maps and monotonicity Original Research Article

We show that given a convex subset KK of a topological vector space XX and a multivalued map T:K⇉X∗T:K⇉X∗, if there exists a straight line SS which is not perpendicular to KK and such that T+wT+w is quasimonotone for each w∈Kw∈K, then TT is monotone. No differentiability or even continuity assumption is imposed; thus we generalize some recent results in the literature.