In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for ...

Let S be a closed oriented surface of genus at least two. Labourie and the author have independently used the theory of hyperbolic affine spheres to find a natural correspondence between convex RP structures on S and pairs (Σ, U) consisting of a conformal structure Σ on S and a holomorphic cubic differential U over Σ. The pairs (Σ, U), for Σ varying in moduli space, allow us to define natural h...

the purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex banach spacehaving a uniformly gateaux differentiable norm. as a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

the purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex banach spacehaving a uniformly gateaux differentiable norm. as a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

Let V be a finite set and M a collection of subsets of V . Then M is an alignment of V if and only if M is closed under taking intersections and contains both V and the empty set. If M is an alignment of V , then the elements of M are called convex sets and the pair (V,M) is called an alignment or a convexity. If S ⊆ V , then the convex hull of S is the smallest convex set that contains S. Supp...

We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.

In the classical model of cooperative games it is generally assumed that there are no restrictions on cooperation and hence, every subset of players is a feasible coalition. However, in many social and economic situations, this model does not apply. Examples are provided by local public goods which are supplied by local communities, social and sports clubs, labor unions, political parties, and ...