Antipodality in convex cones and distance to unpointedness

Antipodality in convex cones and distance to unpointedness

We provide a complete answer to the problem which consists in finding an unpointed convex cone lying at minimal bounded Pompeiu–Hausdorff distance from a pointed one. We give also a simple and useful characterization of the radius of pointedness of a convex cone. A corresponding characterization for the radius of solidity of a convex cone is then derived by using a duality argument. c © 2007 El...

Rough convex cones and rough convex fuzzy cones

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

Some Results on Boundedness in Locally Convex Cones

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...