Let f : X ! IR f+1g be a lower semicontinuous function on a Banach space X. We show that f is quasiconvex if and only if its Clarke subdiierential @f is quasimonotone. As an immediate consequence, we get that f is convex if and only if @f is monotone.

We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and, more generally,M-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set S. We give a counterexample showing that regularity of S in the sense of Clarke is not sufficient for asymptotic equivalence of √ n-consistent locally optimal M-estimato...

We will show that a statistical manifold $$(M, g, \nabla )$$ has constant curvature if and only it is projectively flat conjugate symmetric manifold, is, the affine connection $$\nabla $$ curvatures satisfies $$R=R^*$$ , where $$R^*$$ of dual ^*$$ . Moreover, we properly convex structures on compact induces $$-1$$ vice versa.

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...