Class Of Convex Sets Research Articles

Eine Bemerkung �ber a-priori-fixpunkte nicht-expansiver Abbildungen

For a certain class of convex sets K in normed spaces a generalized center isdefined such that every non-expansive mapping ϕ:K→K with co ϕ(K)⊃K has this center as a fixed point.

Classes of convex sets as generalized metrical spaces

The metrization of classes of convex bodies is generalized to a Minkowski space with unsymmetric metric.

A characteristic property of a class of convex sets

A characteristic property of a class of convex sets

A pre-hilbert space consisting of classes of convex sets

An equivalence relation is defined in the set of all bounded closed convex sets in Euclidean spaceEn. The equivalence classes are shown to be elements of a pre-Hilbert spaceAn, and geometrical relationships betweenAn andEn are investigated.