Displaying similar documents to “Minimal pairs of compact convex sets”

Minimal pairs of bounded closed convex sets

J. Grzybowski, R. Urbański (1997)

Studia Mathematica

Similarity:

The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.

On the reduction of pairs of bounded closed convex sets

J. Grzybowski, D. Pallaschke, R. Urbański (2008)

Studia Mathematica

Similarity:

Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The...

Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces

Jerzy Grzybowski, Diethard Pallaschke, Ryszard Urbański (2009)

Banach Center Publications

Similarity:

The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.

Pairs of sets with convex union.

Ryszard Urbanski (1997)

Collectanea Mathematica

Similarity:

In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.

On reduced pairs of bounded closed convex sets.

Jerzy Grzybowski, Ryszard Urbanski (2003)

Revista Matemática Complutense

Similarity:

In this paper certain criteria for reduced pairs of bounded closed convex set are presented. Some examples of reduced and not reduced pairs are enclosed.