The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or −1, then the ...

We give quantitative versions of strong convergence results due to Baillon, Bruck and Reich for iterations of nonexpansive odd (and more general) operators in uniformly convex Banach spaces.

Suppose C is a nonempty closed convex subset of real Hilbert space H . Let T : C → H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn = (1−αn)u+αnT[(1− βn)xn + βnTxn], yn = (1−αn)u+αnPT[(1− βn)yn + βnPTyn], and zn = P[(1 − αn)u + αnTP[(1 − βn)zn + βnTzn]], where {αn} ⊆ (0...

We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks whether if M is a compact metric space and 0 < α < 1, it is always true the space of Hölder continuous functions of class α is isomorphic to `∞. We show that, on the contrary...

We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space A d S 3 , which are defined as intersection of projective model with a convex polyhedron RP whose vertices all outside and edges meet . show that uniquely determined by their combinatorics dihedral angles, well induced metric on boundary together an additional combinatorial data, describe possible angles metrics boundary.

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all càdlàg processes that are adapted to a given filtration. We show that if such risk measures are required to be real-valued, th...

We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.

A subgraph H of an acyclic digraph D is convex if there is no directed path between vertices of H which contains an arc not in H. A digraph D is connected if the underlying undirected graph of D is connected. We construct an algorithm for enumeration of all connected convex subgraphs of a connected acyclic digraph D of order n. The time complexity of the algorithm is O(n · cc(D)), where cc(D) i...

Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂ n=1 Cn, when this intersection is non-empty. In this talk we discuss projection algorithms for finding such a feasibility point. These algorithms have wide ranging applications including: solutions to convex inequalities, minimization of convex nonsmo...