An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection from e to X has fixed cardinality n+1 ( arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection from e to X where X is a compact subset of .
We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals.
In this study, we introduce a new class of function called geodesic semi E-b-vex functions and generalized geodesic semi E-b-vex functions and discuss some of their properties.
We show that n-dimensional spaces with maximal projection constants exist not only as subspaces of but also as subspaces of l₁. They are characterized by a rigid set of vector conditions. Nevertheless, we show that, in general, there are many non-isometric spaces with maximal projection constants. Several examples are discussed in detail.