Let f be a continuous function on Rn, and suppose f is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which f is not differentiable. Of particular interest is the case where f is not convex, and perhaps not even locally Lipschitz, but is a function whose gradient is easily computed where it is defined. We p...

We consider the truncated K-moment problem when K ⊆ Rn is the closure of a, not necessarily bounded, open set (which includes the important cases K = Rn and K = Rn+). We completely characterize the interior of the convex cone of finite sequences that have a representing measure on K ⊆ Rn. It is in fact the domain of the Legendre-Fenchel transform associated with a certain convex function. And s...

let $c_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{d}$. each function $f in c_{0}(alpha)$ maps the unit disk $mathbb{d}$ onto the complement of an unbounded convex set. in this paper, we study the mapping properties of this class under integral operators.

The goal of this paper is to introduce the approximated convex envelope of a function and to estimate how it differs from its convex envelope. Such a problem arises in various physical situations where the function considered is some energy that has to be minimized.This study is a first step toward understanding how to approximate the quasi-convex envelope of a function. The importance of this ...

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 ...

Let be a d-dimensional simplex with vertices v 0 ; ; v d and B n (f;) denote the n th degree Bernstein polynomial of a continuous function f on. Dahmen and Micchelli 4] proved that B n (f;) B n+1 (f;); n 2 N; for any convex function f on , and it is clear that a necessary and suucient condition for the inequality to become an identity for all n 2 N is that f is an aane polynomial. Let m be the ...