The convexity properties of the kernel O. Also, lower bounds for the Tunin differences involving the moments of <ll(t) are established. The paper concludes with several questions and open problems.

We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.

The purpose of this paper is to introduce general C-convex and C-concave conditions, and then to prove two existence theorems of Nash equilibria in generalized games with C-concavity. Our results generalize the corresponding results due to Nash, Forgó, Takahashi and Kim–Lee in several ways. 2005 Elsevier Ltd. All rights reserved.

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

the objective of this paper is to deal with the fuzzy conic program- ming problems. the aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. toward this end, the convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. un- der this setting, duality t...

This is a survey of the results in [1, 2, 3, 4, 5, 6] on convexity numbers of closed sets in Rn, homogeneity numbers of continuous colorings on Polish spaces and families of functions covering Rn. 1. Convexity numbers of closed sets in R A natural way to measure the degree of non-convexity of a subset S of a real vector space is the convexity number γ(S), the least size of a family C of convex ...

Let Ω be a bounded C∞-smoothly bounded domain in C. For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set W of weakly pseudo-convex points on ∂Ω is small with respect to Minkowski dimension: near each point in the boundary ∂Ω, there is at least one complex tangent direction in which the slices of W has a upper Minkowski dimension stri...

We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. N...

Let Ω be a bounded C∞-smoothly bounded domain in C. For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set W of weakly pseudo-convex points on ∂Ω is small with respect to Minkowski dimension: near each point in the boundary ∂Ω, there is at least one complex tangent direction in which the slices of W has a upper Minkowski dimension stri...