In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...

Given a subset S of R, the Helly number h(S) is the largest size of an inclusionwise minimal family of convex sets whose intersection is disjoint from S. A convex set is S-free if its interior contains no point of S. The parameter f(S) is the largest number of maximal faces in an inclusionwise maximal S-free convex set. We study the relation between the parameters h(S) and f(S). Our main result...

We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p ≥ 1 (resp. p = 0), and some closed subse...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

Given a quasi-concave-convex function f : X × Y → R defined on the product of two convex sets we would like to know if infY supX f = supX infY f . In [4] we showed that that question is very closely linked to the following “reconstruction” problem: given a polytope (i.e. the convex hull of a finite set of points) X and a family F of subpolytopes of X, we would like to know if X ∈ F, knowing tha...

Let B (resp. K , BC , K C ) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B stand for the set of all F ∈ B such that the problem (F,G) is well-posed. We proved that, if X is strictly convex and Kadec, the set ...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...