In this paper we study the concept of Latin-majorizati-\on. Geometrically this concept is different from other kinds of majorization in some aspects. Since the set of all $x$s Latin-majorized by a fixed $y$ is not convex, but, consists of union of finitely many convex sets. Next, we hint to linear preservers of Latin-majorization on $ mathbb{R}^{n}$ and ${M_{n,m}}$.

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

The notion of a generalized convex space we work with in this paper was introduced by Park and Kim in [10]. In generalized convex spaces, many results on fixed points, coincidence points, equilibrium problems, variational inequalities, continuous selections, saddle points, and others have been obtained, see, for example, [6, 8, 10–13]. In this paper, we obtain an almost coincidence point theore...

We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.

In this paper we present several results on the expected complexity of a convex hull of n points chosen uniformly and independently from a convex shape. (i) We show that the expected number of vertices of the convex hull of n points, chosen uniformly and independently from a disk is O(n1/3), and O(k log n) for the case a convex polygon with k sides. Those results are well known (see [RS63, Ray7...

In set theoretic image recovery, the constraints which do not yield convex sets in the chosen Hilbert solution space cannot be enforced. In some cases, however , such constraints may yield convex sets in other Hilbert spaces. In this paper we introduce a generalized product space formalism, through which constraints that are convex in diierent Hilbert spaces can be combined. A nonconvex problem...

In this paper we address the issue of providing a geometrical characterization for the decision problem of asking whether a partial assignment β : fi 7→ αi mapping fuzzy events fi into real numbers αi (i = 1, . . . , n) extends to a generalized belief function on fuzzy sets, according to a suitable definition. We will characterize this problem in a way that allows to treat it as the membership ...

It is well known that the set of possible degree sequences for a simple graph on n vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequences for a simple k-uniform hypergraph on n vertices is not the intersection of a lattice and a convex polytope for k > 3 and n > k + 13. We also show an analogous nonconvexity result for the set of degre...

with n, m > 2, Ω ⊂ R, m < p <∞ and a compact set A ⊂ R with nonempty interior. In the case of a convex integrand f(s, ξ, · ) and a convex restriction set A = K, the global minimizers of (1.1) − (1.3) satisfy optimality conditions in the form of Pontryagin’s principle 01) even though the usual regularity condition for the equality operator (1.2) fails. 02) The question arises whether the Pontrya...