In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. particular, define the so-called radical and study their properties. We will see that such are bounded above curves, rather than straight lines. Applications including discrete continuous Jensen inequalities, subadditivity behavior, Hermite–Hadamard integral inequalities be ...

we provide a continuous representation of quasi-concave mappings by their upper level sets. A possible motivation is the extension to quasi-concave mappings of a result by Ulam and Hyers, which states that every approximately convex mapping can be approximated by a convex mapping. Keyword: quasi-concave, upper level set AMS classification: 47N10

This study characterizes the concavity properties of Jorgenson and Slesnick’s social welfare function that is likely most empirically relevant among family “long” functions. We bridge this knowledge gap using definition generalized to show conditions necessary for long interest be decreasing quasi-convex with respect prices. Thanks result, functions regular curvature can suitable applied analys...

This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in R. These results were known for the convex case and played an essential role in the development of the theory. Because duality relations cannot be applied in the quasi-convex setting, new ingredients were introduced that give new understanding for the conv...

Many combinatorial optimization problems can be formulated as: for a given set system over E (i.e., for a pair (E, ) where ⊆ 2E is a family of feasible subsets of finite set E), and for a given function F : →R, find an element of for which the value of the function F is minimum or maximum. In general, this optimization problem is NP-hard, but for some specific functions and set systems the prob...

A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, are introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and extrinsic diameter functions for finitely presented groups. We show that the existence of a (finite-valued) tame filling function implies that the group is tame...