New results on approximation of a convex body K ⊂ R3 by affine images of circular cylinders, parallelepipeds, hexagonal and octagonal regular (and some other) prisms are obtained. Two of the theorems obtained are as follows (V (K) denotes the volume of a body K ⊂ R3). Theorem 1. Let K be an arbitrary convex body in R3. There exists a regular octagonal prism an affine image of which is circumscr...

This paper is to characterize L-concavities and L-convexities via some derived forms of relations operators. Specifically, notions L-concave internal relation space hull are introduced. It proved that the category L-concave
 spaces isomorphic spaces. Also, L-convex enclosed

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

For functions defined on integer lattice points, discrete versions of the Hessian matrix have been considered in various contexts. In discrete convex analysis, for example, certain combinatorial properties of the discrete Hessian matrices are known to characterize M-convex and L-convex functions, which can be extended to convex functions in real variables. The relationship between convex extens...

Given a class $${{\mathcal {P}}}$$ of Banach spaces, locally convex space (LCS) E is called multi- if can be isomorphically embedded into product spaces that belong to . We investigate the question whether free L(X) strongly nuclear, Schwartz, multi-Hilbert or multi-reflexive. If X Tychonoff containing an infinite compact subset then, as it follows from results Außenhofer (Topol Appl 134:90–102...

As topology-like mathematical structures, convex structures can be characterized by betweenness relations via (restricted) hull operators in spaces. In a topological approach, the aim of this paper is to present fuzzy counterpart based on points Concretely, notion L-betweenness restricted L-hull introduced. Firstly, it proved that are categorically isomorphic and L-remotehood systems, respectiv...

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...