Let M be a compact manifold of dimension n with a strictly convex projective structure. We consider the geodesic flow of the Hilbert metric on it which is known to be Anosov. We prove that its topological entropy is less than n − 1, with equality if and only if the structure is Riemannian, that is hyperbolic. As a corollary, we get that the volume entropy of a divisible strictly convex set is l...

We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasinormal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. ...

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

This supplement provides the proof for all the theorems and corollaries in the main paper. We provide the proofs as well as the theorem statements for the ease of understanding while borrowing the notation from the main draft. Proof. Assume that we are given an > 0 for which the condition mentioned in the theorem statement holds true (for the sake of simplicity we assume the same for all w ∈ R ...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

In that paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem. In the illustration, we have given a refinement to obtain this solution.

Let (M, ∂M) be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. We are interested in the following question: Question A Let h be a (non-smooth) metric on ∂M , with curvature K > −1. Is there a unique hyperbolic metric g on M , with convex boundary, such that the induced metric on ∂M is h ? There is also a dual statement: Question B Let h be a (non...

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 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 ...