Much of the recent literature on risk measures is concerned with essentially bounded risks in L∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on Lp spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk me...

In this paper, we introduce the concept of convex structure in generalized fuzzy metric spaces and proved common fixed point theorems for a pair self-mappings under sufficient contractive type conditions.

All GL (n) covariant star-body-valued valuations on convex polytopes are completely classified. It is shown that there is a unique nontrivial such valuation. This valuation turns out to be the so-called “intersection operator”—an operator that played a critical role in the solution of the Busemann-Petty problem. Introduction. A function Z defined on the set K of convex bodies (that is, of conve...

We study succinct approximation of functions that have noisy oracle access. Namely, construction of a succinct representation of a function, given oracle access to an L-approximation of the function, rather than to the function itself. Specifically, we consider the question of the succinct representation of an approximation of a convex function φ that cannot be accessed directly, but only via o...

This paper presents the concepts of (L,M)-remotehood spaces and (L,M)-convergence in framework (L,M)-fuzzy convex spaces. Firstly, it is shown that category isomorphic to Secondly, proved can be embedded as a reflective subcategory. Finally, preconvex (L,M)- convergence are introduced

Finding the minimum vertex distance between two dis-joint convex polygons in linear time. [6] Supowit, K. J.: The relative neighborhood graph, with an application to minimum spanning trees. A note on the all-nearest-neighbor problem for convex polygons. [10] O'Rourke, J., et al.: A new linear algorithm for intersecting convex polygons.Since P nw and Q R are two linearly separable convex polygon...